Pub Date : 2019-01-17DOI: 10.17323/1609-4514-2019-19-2-343-356
A. Klimenko
We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a sufficiently regular (e.g., Lipschitz) function have the same asymptotic behavior of distributions as the behaviour of ergodic integrals for a generic translation flow on a flat surface, described by A. Bufetov.
{"title":"Spatial Limit Theorem for Interval Exchange Transformations","authors":"A. Klimenko","doi":"10.17323/1609-4514-2019-19-2-343-356","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-343-356","url":null,"abstract":"We prove a spatial limit theorem for generic interval exchange transformations (IETs): for a generic IET the normalized ergodic sums of a sufficiently regular (e.g., Lipschitz) function have the same asymptotic behavior of distributions as the behaviour of ergodic integrals for a generic translation flow on a flat surface, described by A. Bufetov.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49053369","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 : 2019-01-01DOI: 10.17323/1609-4514-2019-19-1-133-151
S. Poghosyan, H. Zessin
{"title":"Cluster Representations of Classical and Quantum Processes","authors":"S. Poghosyan, H. Zessin","doi":"10.17323/1609-4514-2019-19-1-133-151","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-1-133-151","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824114","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 : 2019-01-01DOI: 10.17323/1609-4514-2019-19-1-3-5
V. M. Tikhomirov
{"title":"Young Bob Minlos","authors":"V. M. Tikhomirov","doi":"10.17323/1609-4514-2019-19-1-3-5","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-1-3-5","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824975","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 : 2019-01-01DOI: 10.17323/1609-4514-2019-19-1-51-76
C. Boldrighini, A. Pellegrinotti, E. Zhizhina
{"title":"Regular and Singular Continuous Time Random Walk in Dynamic Random Environment","authors":"C. Boldrighini, A. Pellegrinotti, E. Zhizhina","doi":"10.17323/1609-4514-2019-19-1-51-76","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-1-51-76","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67824993","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 : 2019-01-01DOI: 10.17323/1609-4514-2019-19-1-77-88
B. Gurevich, S. Komech, A. Tempelman
{"title":"Random Averaging in Ergodic Theorem and Boundary Deformation Rate in Symbolic Dynamics","authors":"B. Gurevich, S. Komech, A. Tempelman","doi":"10.17323/1609-4514-2019-19-1-77-88","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-1-77-88","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67825094","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 : 2018-12-20DOI: 10.17323/1609-4514-2022-22-2-177-224
Andrea J. Appel, Francesco Sala, O. Schiffmann
We introduce a new class of infinite-dimensional Lie algebras, which arise as continuum colimits of Borcherds-Kac-Moody algebras. They are associated with a topological generalization of the notion of quiver, where vertices are replaced by intervals in a real one-dimensional topological space, and are described by a continuum root system with no simple root. For these Lie algebras, we prove an analogue of the Gabber-Kac-Serre theorem, providing a complete set of defining relations featuring only quadratic Serre relations.
{"title":"Continuum Kac–Moody Algebras","authors":"Andrea J. Appel, Francesco Sala, O. Schiffmann","doi":"10.17323/1609-4514-2022-22-2-177-224","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-2-177-224","url":null,"abstract":"We introduce a new class of infinite-dimensional Lie algebras, which arise as continuum colimits of Borcherds-Kac-Moody algebras. They are associated with a topological generalization of the notion of quiver, where vertices are replaced by intervals in a real one-dimensional topological space, and are described by a continuum root system with no simple root. For these Lie algebras, we prove an analogue of the Gabber-Kac-Serre theorem, providing a complete set of defining relations featuring only quadratic Serre relations.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45958327","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 : 2018-12-01DOI: 10.17323/1609-4514-2018-18-4-607-616
C. Bartolone, A. Bartolo, G. Falcone
{"title":"Solvable Extensions of Nilpotent Complex Lie Algebras of Type 2n,1,1","authors":"C. Bartolone, A. Bartolo, G. Falcone","doi":"10.17323/1609-4514-2018-18-4-607-616","DOIUrl":"https://doi.org/10.17323/1609-4514-2018-18-4-607-616","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45790641","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 : 2018-11-10DOI: 10.17323/1609-4514-2021-21-2-271-286
D. Cerveau, B. Sc'ardua
We study analytic deformations of holomorphic differential 1-forms. The initial 1-form is exact homogeneous and the deformation is by polynomial integrable 1-forms. We investigate under which conditions the elements of the deformation are still exact or, more generally, exhibit a first integral. Our results are related to natural extensions of classical results of Ilyashenko on limit cycles of perturbations of hamiltonian systems in two complex variables.
{"title":"Integrable Deformations of Foliations: a Generalization of Ilyashenko's Result","authors":"D. Cerveau, B. Sc'ardua","doi":"10.17323/1609-4514-2021-21-2-271-286","DOIUrl":"https://doi.org/10.17323/1609-4514-2021-21-2-271-286","url":null,"abstract":"We study analytic deformations of holomorphic differential 1-forms. The initial 1-form is exact homogeneous and the deformation is by polynomial integrable 1-forms. We investigate under which conditions the elements of the deformation are still exact or, more generally, exhibit a first integral. Our results are related to natural extensions of classical results of Ilyashenko on limit cycles of perturbations of hamiltonian systems in two complex variables.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41688176","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 : 2018-10-29DOI: 10.17323/1609-4514-2019-19-1-107-120
E. Pechersky, S. Pirogov, G. Schutz, A. Vladimirov, A. Yambartsev
We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a constant rate (pumping). The number of excited particles decreases by means of photon emission through interactions of the particles. We analyse the rare event of flashes, i.e., the emission of a very large number of photons $B$ during a fixed time interval $T$. We employ the theory of large deviations to provide the asymptotics of the probability of such event when the total number of particles $N$ tends to infinity. This theory gives us also the optimal trajectory of scaled process corresponding to this event. The stationary regime of this process we call the large emission regime. In several cases we prove that in the large emission regime a share of excited particles in a system is stable under the changes of the pumping and emission rates.
{"title":"Large Emission Regime in Mean Field Luminescence","authors":"E. Pechersky, S. Pirogov, G. Schutz, A. Vladimirov, A. Yambartsev","doi":"10.17323/1609-4514-2019-19-1-107-120","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-1-107-120","url":null,"abstract":"We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a constant rate (pumping). The number of excited particles decreases by means of photon emission through interactions of the particles. We analyse the rare event of flashes, i.e., the emission of a very large number of photons $B$ during a fixed time interval $T$. We employ the theory of large deviations to provide the asymptotics of the probability of such event when the total number of particles $N$ tends to infinity. This theory gives us also the optimal trajectory of scaled process corresponding to this event. The stationary regime of this process we call the large emission regime. In several cases we prove that in the large emission regime a share of excited particles in a system is stable under the changes of the pumping and emission rates.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45795335","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 : 2018-10-22DOI: 10.17323/1609-4514-2019-19-2-217-274
A. Bufetov, P. Nikitin, Yanqi Qiu
Our first result states that the orthogonal and symplectic Bessel processes are rigid in the sense of Ghosh and Peres. Our argument in the Bessel case proceeds by an estimate of the variance of additive statistics in the spirit of Ghosh and Peres. Second, a sufficient condition for number rigidity of stationary Pfaffian processes, relying on the Kolmogorov criterion for interpolation of stationary processes and applicable, in particular, to pfaffian sine-processes, is given in terms of the asymptotics of the spectral measure for additive statistics.
{"title":"On Number Rigidity for Pfaffian Point Processes","authors":"A. Bufetov, P. Nikitin, Yanqi Qiu","doi":"10.17323/1609-4514-2019-19-2-217-274","DOIUrl":"https://doi.org/10.17323/1609-4514-2019-19-2-217-274","url":null,"abstract":"Our first result states that the orthogonal and symplectic Bessel processes are rigid in the sense of Ghosh and Peres. Our argument in the Bessel case proceeds by an estimate of the variance of additive statistics in the spirit of Ghosh and Peres. Second, a sufficient condition for number rigidity of stationary Pfaffian processes, relying on the Kolmogorov criterion for interpolation of stationary processes and applicable, in particular, to pfaffian sine-processes, is given in terms of the asymptotics of the spectral measure for additive statistics.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48156970","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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