Pub Date : 2022-09-13DOI: 10.1142/s2010326322990015
{"title":"Author index Volume 11 (2022)","authors":"","doi":"10.1142/s2010326322990015","DOIUrl":"https://doi.org/10.1142/s2010326322990015","url":null,"abstract":"","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76368425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-19DOI: 10.1142/s2010326323500107
D. Beck
In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a random Gram determinant.
{"title":"On the fourth moment of a random determinant","authors":"D. Beck","doi":"10.1142/s2010326323500107","DOIUrl":"https://doi.org/10.1142/s2010326323500107","url":null,"abstract":"In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a random Gram determinant.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90327855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-27DOI: 10.1142/s2010326322500435
Yun Li, B. Valkó
We prove an operator level limit for the circular Jacobi β-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the normalized characteristic polynomials converge to a random analytic function, which we characterize via the joint distribution of its Taylor coefficients at zero and as the solution of a stochastic differential equation system. We also provide analogous results for the real orthogonal β-ensemble.
{"title":"Operator level limit of the circular Jacobi β-ensemble","authors":"Yun Li, B. Valkó","doi":"10.1142/s2010326322500435","DOIUrl":"https://doi.org/10.1142/s2010326322500435","url":null,"abstract":"We prove an operator level limit for the circular Jacobi β-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the normalized characteristic polynomials converge to a random analytic function, which we characterize via the joint distribution of its Taylor coefficients at zero and as the solution of a stochastic differential equation system. We also provide analogous results for the real orthogonal β-ensemble.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75499297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-15DOI: 10.1142/s2010326323500028
J. Andrade, C. G. Best
In this paper, we give an analytic proof of the asymptotic behavior of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order coefficients previously found by Assiotis, Bailey and Keating. We also discuss the conjectures of Bailey and Keating for the corresponding moments of moments of [Formula: see text]-functions with symplectic and orthogonal symmetry. Specifically, we show that these conjectures follow from the shifted moments conjecture of Conrey, Farmer, Keating, Rubinstein and Snaith.
{"title":"Random matrix theory and moments of moments of L-functions","authors":"J. Andrade, C. G. Best","doi":"10.1142/s2010326323500028","DOIUrl":"https://doi.org/10.1142/s2010326323500028","url":null,"abstract":"In this paper, we give an analytic proof of the asymptotic behavior of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order coefficients previously found by Assiotis, Bailey and Keating. We also discuss the conjectures of Bailey and Keating for the corresponding moments of moments of [Formula: see text]-functions with symplectic and orthogonal symmetry. Specifically, we show that these conjectures follow from the shifted moments conjecture of Conrey, Farmer, Keating, Rubinstein and Snaith.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73815460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-29DOI: 10.1142/s201032632250037x
N. Ercolani, Patrick Waters
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of construction developed here involves a novel asymptotic symbol calculus for difference operators based on the relation between spectral asymptotics for Hermitian random matrices and asymptotics of orthogonal polynomials with exponential weights. These closed form expressions have a universal character in the sense that they are independent of the explicit valence distribution of the cellular networks within a broad class. Nevertheless the valence distributions may be recovered from the closed form generating functions by a remarkable unwinding identity in terms of Appell polynomials generated by Bessel functions. Our treatment reveals the generating functions to be solutions of nonlinear conservation laws and their prolongations. This characterization enables one to gain insights that go beyond more traditional methods that are purely combinatorial. Universality results are connected to stability results for characteristic singularities of conservation laws that were studied by Caflisch, Ercolani, Hou and Landis, Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems, Commun. Pure Appl. Math. 46 (1993) 453–499, as well as directly related to universality results for random matrix spectra.
{"title":"Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials","authors":"N. Ercolani, Patrick Waters","doi":"10.1142/s201032632250037x","DOIUrl":"https://doi.org/10.1142/s201032632250037x","url":null,"abstract":"Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of construction developed here involves a novel asymptotic symbol calculus for difference operators based on the relation between spectral asymptotics for Hermitian random matrices and asymptotics of orthogonal polynomials with exponential weights. These closed form expressions have a universal character in the sense that they are independent of the explicit valence distribution of the cellular networks within a broad class. Nevertheless the valence distributions may be recovered from the closed form generating functions by a remarkable unwinding identity in terms of Appell polynomials generated by Bessel functions. Our treatment reveals the generating functions to be solutions of nonlinear conservation laws and their prolongations. This characterization enables one to gain insights that go beyond more traditional methods that are purely combinatorial. Universality results are connected to stability results for characteristic singularities of conservation laws that were studied by Caflisch, Ercolani, Hou and Landis, Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems, Commun. Pure Appl. Math. 46 (1993) 453–499, as well as directly related to universality results for random matrix spectra.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74889116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-19DOI: 10.1142/s2010326322500381
Zerui Tao, Zhouping Li
Recently, tensors are widely used to represent higher-order data with internal spatial or temporal relations, e.g. images, videos, hyperspectral images (HSIs). While the true signals are usually corrupted by noises, it is of interest to study tensor recovery problems. To this end, many models have been established based on tensor decompositions. Traditional tensor decomposition models, such as the CP and Tucker factorization, treat every mode of tensors equally. However, in many real applications, some modes of the data act differently from the other modes, e.g. channel mode of images, time mode of videos, band mode of HSIs. The recently proposed model called t-SVD aims to tackle such problems. In this paper, we focus on tensor denoising problems. Specifically, in order to obtain low-rank estimators of true signals, we propose to use different shrinkage functions to shrink the tensor singular values based on the t-SVD. We derive Stein’s unbiased risk estimate (SURE) of the proposed model and develop adaptive SURE-based tuning parameter selection procedure, which is totally data-driven and simultaneous with the estimation process. The whole modeling procedure requires only one round of t-SVD. To demonstrate our model, we conduct experiments on simulation data, images, videos and HSIs. The results show that the proposed SURE approximates the true risk function accurately. Moreover, the proposed model selection procedure picks good tuning parameters out. We show the superiority of our model by comparing with state-of-the-art denoising models. The experiments manifest that our model outperforms in both quantitative metrics (e.g. RSE, PSNR) and visualizing results.
{"title":"Adaptive singular value shrinkage estimate for low rank tensor denoising","authors":"Zerui Tao, Zhouping Li","doi":"10.1142/s2010326322500381","DOIUrl":"https://doi.org/10.1142/s2010326322500381","url":null,"abstract":"Recently, tensors are widely used to represent higher-order data with internal spatial or temporal relations, e.g. images, videos, hyperspectral images (HSIs). While the true signals are usually corrupted by noises, it is of interest to study tensor recovery problems. To this end, many models have been established based on tensor decompositions. Traditional tensor decomposition models, such as the CP and Tucker factorization, treat every mode of tensors equally. However, in many real applications, some modes of the data act differently from the other modes, e.g. channel mode of images, time mode of videos, band mode of HSIs. The recently proposed model called t-SVD aims to tackle such problems. In this paper, we focus on tensor denoising problems. Specifically, in order to obtain low-rank estimators of true signals, we propose to use different shrinkage functions to shrink the tensor singular values based on the t-SVD. We derive Stein’s unbiased risk estimate (SURE) of the proposed model and develop adaptive SURE-based tuning parameter selection procedure, which is totally data-driven and simultaneous with the estimation process. The whole modeling procedure requires only one round of t-SVD. To demonstrate our model, we conduct experiments on simulation data, images, videos and HSIs. The results show that the proposed SURE approximates the true risk function accurately. Moreover, the proposed model selection procedure picks good tuning parameters out. We show the superiority of our model by comparing with state-of-the-art denoising models. The experiments manifest that our model outperforms in both quantitative metrics (e.g. RSE, PSNR) and visualizing results.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77970709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-12DOI: 10.1142/s2010326322500289
A. Ammar, A. Jeribi, B. Saadaoui
In this paper, a new concept for a [Formula: see text] block relation matrix is studied in a Banach space. It is shown that, under certain condition, we can investigate the Frobenius–Schur decomposition of relation matrices. Furthermore, we present some conditions which should allow the multivalued [Formula: see text] matrices linear operator to be closable.
{"title":"A new decomposition for multivalued 3 × 3 matrices","authors":"A. Ammar, A. Jeribi, B. Saadaoui","doi":"10.1142/s2010326322500289","DOIUrl":"https://doi.org/10.1142/s2010326322500289","url":null,"abstract":"In this paper, a new concept for a [Formula: see text] block relation matrix is studied in a Banach space. It is shown that, under certain condition, we can investigate the Frobenius–Schur decomposition of relation matrices. Furthermore, we present some conditions which should allow the multivalued [Formula: see text] matrices linear operator to be closable.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80853675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-05DOI: 10.1142/s2010326322500356
P. Forrester
The loop equations for the [Formula: see text]-ensembles are conventionally solved in terms of a [Formula: see text] expansion. We observe that it is also possible to fix [Formula: see text] and expand in inverse powers of [Formula: see text]. At leading order, for the one-point function [Formula: see text] corresponding to the average of the linear statistic [Formula: see text] and after specialising to the classical weights, this reclaims well known results of Stieltjes relating the zeros of the classical polynomials to the minimum energy configuration of certain log–gas potential energies. Moreover, it is observed that the differential equations satisfied by [Formula: see text] in the case of classical weights — which are particular Riccati equations — are simply related to the differential equations satisfied by [Formula: see text] in the high temperature scaled limit [Formula: see text] ([Formula: see text] fixed, [Formula: see text]), implying a certain high–low temperature duality. A generalisation of this duality, valid without any limiting procedure, is shown to hold for [Formula: see text] and all its higher point analogues in the classical [Formula: see text]-ensembles.
{"title":"High–low temperature dualities for the classical β-ensembles","authors":"P. Forrester","doi":"10.1142/s2010326322500356","DOIUrl":"https://doi.org/10.1142/s2010326322500356","url":null,"abstract":"The loop equations for the [Formula: see text]-ensembles are conventionally solved in terms of a [Formula: see text] expansion. We observe that it is also possible to fix [Formula: see text] and expand in inverse powers of [Formula: see text]. At leading order, for the one-point function [Formula: see text] corresponding to the average of the linear statistic [Formula: see text] and after specialising to the classical weights, this reclaims well known results of Stieltjes relating the zeros of the classical polynomials to the minimum energy configuration of certain log–gas potential energies. Moreover, it is observed that the differential equations satisfied by [Formula: see text] in the case of classical weights — which are particular Riccati equations — are simply related to the differential equations satisfied by [Formula: see text] in the high temperature scaled limit [Formula: see text] ([Formula: see text] fixed, [Formula: see text]), implying a certain high–low temperature duality. A generalisation of this duality, valid without any limiting procedure, is shown to hold for [Formula: see text] and all its higher point analogues in the classical [Formula: see text]-ensembles.","PeriodicalId":54329,"journal":{"name":"Random Matrices-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85799654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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