Заседания семинаров
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Наталья Смородина
О некоторых свойствах дробной производной броуновского локального времени.
М. В. Нещадим реферирует статью (продолжение):
Hosszu Miklos: Nemszimmetrikus kozepertekek.
MTA Alkalmazott Matematikai Intezetenek Kozlemenyei, VII. evf. (1957) 207-218.
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Siyao Yin (Mathematical Center in Akademgorodok)
Generalized Hermitian Matrix Model: Statistical Physics Insights.
Аннотация
This study, conducted in collaboration with Professor Jian Zhou, explores a generalized Hermitian one-matrix model derived from a sequence of real numbers, representing moments for a probability distribution on the real line. We establish that the model’s partition function is a tau-function of the KP hierarchy and the Toda lattice hierarchy. Under specific conditions on the probability distribution, the partition function satisfies Virasoro constraints. For concrete examples, we use moments from various statistical models, revealing intriguing correspondences: Boltzmann statistics aligns with the Dirac delta distribution, Acharya-Swamy statistics with the Gamma distribution (encompassing Fermi-Dirac and Bose-Einstein statistics), exponential polynomial model with the Poisson distribution, and Bessel polynomial model with the inverse Gauss distribution. Notably, Acharya-Swamy statistics, linked to the two-parameter Gamma distribution, exhibits captivating phase transition and symmetry phenomena. We establish a connection between Acharya-Swamy statistics and Grothendieck’s dessins d’enfants/Laguerre unitary ensemble through the Gamma distribution.М. И. Марчук
Реферат статьи:
U. Andrews, A. M. Kach
Computing and dominating the Ryll-Nardzewski function.
Dong W. (Shanghai, People's Republic of China)
Observer-based stabilization for discrete-time quasi-one-sided Lipschitz nonlinear time-delay systems.
О. Ошмарина
Полином Александера для заузленных графов.