We describe a Yang–Baxter integrable vertex model, which can be realized as a degeneration of a vertex model introduced by Aggarwal, Borodin, and Wheeler (2021). From this vertex model, we construct a certain class of partition functions that we show are essentially equal to the super ribbon functions of Lam. Using the vertex model formalism, we give proofs of many properties of these polynomials, namely a Cauchy identity and generalizations of known identities for supersymmetric Schur polynomials.
{"title":"A vertex model for supersymmetric LLT polynomials","authors":"Andrew Gitlin, David Keating","doi":"10.4171/aihpd/171","DOIUrl":"https://doi.org/10.4171/aihpd/171","url":null,"abstract":"We describe a Yang–Baxter integrable vertex model, which can be realized as a degeneration of a vertex model introduced by Aggarwal, Borodin, and Wheeler (2021). From this vertex model, we construct a certain class of partition functions that we show are essentially equal to the super ribbon functions of Lam. Using the vertex model formalism, we give proofs of many properties of these polynomials, namely a Cauchy identity and generalizations of known identities for supersymmetric Schur polynomials.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136017911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The groups $mathrm{O}(N)$ and $mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $mathrm{O}(-N)simeqmathrm{Sp}(N)$. This duality has been studied for vector models, $mathrm{SO}(N)$ and $mathrm{Sp}(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two-point function.
{"title":"Duality of orthogonal and symplectic random tensor models","authors":"Razvan Gurau, Hannes Keppler","doi":"10.4171/aihpd/177","DOIUrl":"https://doi.org/10.4171/aihpd/177","url":null,"abstract":"The groups $mathrm{O}(N)$ and $mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $mathrm{O}(-N)simeqmathrm{Sp}(N)$. This duality has been studied for vector models, $mathrm{SO}(N)$ and $mathrm{Sp}(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two-point function.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce $R$-diagonal and even operators of second order. We give a formula for the second order free cumulants of the square $x^2$ of a second order even element in terms of the second order free cumulants of $x$. Similar formulas are proved for the second order free cumulants of $aa^*$, when $a$ is a second order $R$-diagonal operator. We also show that if $r$ is second order $R$-diagonal and $b$ is second order free from $r$, then $rb$ is also second order $R$-diagonal. We present a large number of examples, in particular, the limit distribution of products of Ginibre matrices. We prove the conjectured formula of Dartois and Forrester for the fluctuations moments of the product of two independent complex Wishart matrices and generalize it to any number of factors.
{"title":"Second order cumulants: Second order even elements and $R$-diagonal elements","authors":"Octavio Arizmendi, James A. Mingo","doi":"10.4171/aihpd/176","DOIUrl":"https://doi.org/10.4171/aihpd/176","url":null,"abstract":"We introduce $R$-diagonal and even operators of second order. We give a formula for the second order free cumulants of the square $x^2$ of a second order even element in terms of the second order free cumulants of $x$. Similar formulas are proved for the second order free cumulants of $aa^*$, when $a$ is a second order $R$-diagonal operator. We also show that if $r$ is second order $R$-diagonal and $b$ is second order free from $r$, then $rb$ is also second order $R$-diagonal. We present a large number of examples, in particular, the limit distribution of products of Ginibre matrices. We prove the conjectured formula of Dartois and Forrester for the fluctuations moments of the product of two independent complex Wishart matrices and generalize it to any number of factors.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study perfect matchings on the square-hexagon lattice with $1times n$ periodic edge weights and with one of the following boundary conditions: (1) each remaining vertex on the bottom boundary is followed by $(m-1)$ removed vertices; (2) the bottom boundary can be divided into finitely many alternating line segments, each of which has a fixed positive length in the scaling limit, such that all the vertices along each line segment are either removed or retained. In case (1), we show that under certain homeomorphism from the liquid region to the upper half-plane, the height fluctuations converge to the Gaussian free field in the upper half-plane. In case (2), when the edge weights $x_1,ldots,x_n$ in one period satisfy the condition that $x_{i+1}=O(frac{x_i}{e^{Nalpha}})$, where $alpha>0$ is a constant independent of $N$, we show that the height fluctuations converge to a sum of independent Gaussian free fields.
{"title":"Fluctuations of dimer heights on contracting square-hexagon lattices","authors":"Zhongyang Li","doi":"10.4171/aihpd/174","DOIUrl":"https://doi.org/10.4171/aihpd/174","url":null,"abstract":"We study perfect matchings on the square-hexagon lattice with $1times n$ periodic edge weights and with one of the following boundary conditions: (1) each remaining vertex on the bottom boundary is followed by $(m-1)$ removed vertices; (2) the bottom boundary can be divided into finitely many alternating line segments, each of which has a fixed positive length in the scaling limit, such that all the vertices along each line segment are either removed or retained. In case (1), we show that under certain homeomorphism from the liquid region to the upper half-plane, the height fluctuations converge to the Gaussian free field in the upper half-plane. In case (2), when the edge weights $x_1,ldots,x_n$ in one period satisfy the condition that $x_{i+1}=O(frac{x_i}{e^{Nalpha}})$, where $alpha>0$ is a constant independent of $N$, we show that the height fluctuations converge to a sum of independent Gaussian free fields.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"197 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135109318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we propose a nonparametric estimation strategy for the conditional density function of Y given X , from independent and identically distributed observations ( X i , Y i ) 1 ≤ i ≤ n . We consider a regression strategy related to projection subspaces of L 2 generated by non compactly supported bases. This (cid:28)rst study is then extended to the case where Y is not directly observed, but only Z = Y + ε , where ε is a noise with known density. In these two settings, we build and study collections of estimators, compute their rates of convergence on anisotropic space on non-compact supports, and prove related lower bounds. Then, we consider adaptive estimators for which we also prove risk bounds.
． 本文针对给定X的独立同分布观测值(X i, Y i) 1≤i≤n，提出了Y的条件密度函数的非参数估计策略。我们考虑了一种由非紧支持基生成的l2的投影子空间的回归策略。这(cid:28)第一个研究然后被扩展到没有直接观察到Y，而只有Z = Y + ε的情况，其中ε是已知密度的噪声。在这两种情况下，我们建立和研究了估计量集合，计算了它们在非紧支撑上的各向异性空间上的收敛速率，并证明了相关的下界。然后，我们考虑自适应估计器，我们也证明了风险界限。
{"title":"Non compact estimation of the conditional density from direct or noisy data","authors":"F. Comte, C. Lacour","doi":"10.1214/22-aihp1291","DOIUrl":"https://doi.org/10.1214/22-aihp1291","url":null,"abstract":". In this paper, we propose a nonparametric estimation strategy for the conditional density function of Y given X , from independent and identically distributed observations ( X i , Y i ) 1 ≤ i ≤ n . We consider a regression strategy related to projection subspaces of L 2 generated by non compactly supported bases. This (cid:28)rst study is then extended to the case where Y is not directly observed, but only Z = Y + ε , where ε is a noise with known density. In these two settings, we build and study collections of estimators, compute their rates of convergence on anisotropic space on non-compact supports, and prove related lower bounds. Then, we consider adaptive estimators for which we also prove risk bounds.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"17 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81237160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We consider a particle which performs a dynamical random walk on Z and whose local dynamics is given by expanding maps. We provide sufficient conditions for the position of the particle z n to satisfy the Central Limit Theorem.
{"title":"Dynamical random walk on the integers with a drift","authors":"Dmitry Dolgopyat, D. Karagulyan","doi":"10.1214/22-aihp1300","DOIUrl":"https://doi.org/10.1214/22-aihp1300","url":null,"abstract":". We consider a particle which performs a dynamical random walk on Z and whose local dynamics is given by expanding maps. We provide sufficient conditions for the position of the particle z n to satisfy the Central Limit Theorem.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91240819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we establish the existence and the uniqueness of solutions of stochastic evolution equations (SEEs) with reflection in an infinite dimensional ball. Our framework is sufficiently general to include e.g. the stochastic Navier-Stokes equations.
{"title":"Reflection of stochastic evolution equations in infinite dimensional domains","authors":"Z. Brze'zniak, Tusheng Zhang","doi":"10.1214/22-aihp1294","DOIUrl":"https://doi.org/10.1214/22-aihp1294","url":null,"abstract":"In this paper, we establish the existence and the uniqueness of solutions of stochastic evolution equations (SEEs) with reflection in an infinite dimensional ball. Our framework is sufficiently general to include e.g. the stochastic Navier-Stokes equations.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"35 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74797304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the number of winding turns as the time horizon tends to infinity. In the asymptotic regime, our discrete approach is equivalent to the continuous one studied previously in the literature and our main result extends the existing ones. Our model allows for a general dependence of the coordinates of the process and non-differentiability of one of them. Furthermore, beyond our general framework, we consider as examples an approximation to the winding number of a process whose coordinates are both non-differentiable and the winding number of a process which is not exactly stationary.
{"title":"Winding number for stationary Gaussian processes using real variables","authors":"J.-M. Azaïs, F. Dalmao, J. R. León","doi":"10.1214/22-aihp1278","DOIUrl":"https://doi.org/10.1214/22-aihp1278","url":null,"abstract":"We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the number of winding turns as the time horizon tends to infinity. In the asymptotic regime, our discrete approach is equivalent to the continuous one studied previously in the literature and our main result extends the existing ones. Our model allows for a general dependence of the coordinates of the process and non-differentiability of one of them. Furthermore, beyond our general framework, we consider as examples an approximation to the winding number of a process whose coordinates are both non-differentiable and the winding number of a process which is not exactly stationary.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"58 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84449394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An upper bound for pc in range-R bond percolation in two and three dimensions","authors":"Jieliang Hong","doi":"10.1214/22-aihp1305","DOIUrl":"https://doi.org/10.1214/22-aihp1305","url":null,"abstract":"","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"3 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79868933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.
{"title":"Kudō-continuity of conditional entropies","authors":"M. Björklund, Yair Hartman, Hanna Oppelmayer","doi":"10.1214/22-aihp1313","DOIUrl":"https://doi.org/10.1214/22-aihp1313","url":null,"abstract":". In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"49 7 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75732785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：