Числення Маллявена та його застосування
Голова семінару: Професор Андрій Анатолійович Дороговцев
17.00, кімната 208.
Секретар семінару: Георгій Рябов
Записи доповідей минулих семінарів.
- Семінар 19.11.2024
Доповідач: Катерина Глиняна (Інститут математики НАН України)
Тема: Liouville theorem for the equations with interaction and its application
- Семінар 12.11.2024
Доповідач : Насір Ганіходжаєв (Інститут математики імені В.І. Романовського, Ташкент)
Тема: Quadratic Stochastic Processes with a Continuous Set of States
- Семінар 05.11.2024
Доповідач: Кирило Кучинський (Інститут математики НАН України)
Тема: Asymptotic behavior of the solution to the multi-dimensional stochastic differential equation with interactions
- Семінар 29.10.2024
Доповідач: Микола Портенко (Інститут математики НАН України)
Тема: On the killing coefficient of multidimensional Brownian motion killed at the hitting time of a given hypersurface
- Семінар 22.10.2024
Доповідач: Андрій А. Дороговцев (Інститут математики НАН України, спільна робота з Naoufel Salhi, Кайруанський університет)
Тема: Universal generalized functionals
- Семінар 08.10.2024
Доповідач: Микола Вовчанський (Інститут математики НАН України)
Тема: On multidimensional point densities for Arratia flows with drift
- Семінар 01.10.2024
Доповідач: Вадим Радченко (Київський національний університет імені Тараса Шевченка)
Тема: Equations with a symmetric integral with respect to stochastic measures
Тези. The stochastic measures (SMs) are sigma-additive in probability random set functions defined on a sigma-algebra. Many important classes of processes generate a SM. In the talk, we give a definition of the Stratonovich-type integral with respect to SM and study some equations with this integral. The averaging principle for these equations will be considered.
- Семінар 24.09.2024
Доповідач: Олексій Руденко (Інститут математики НАН України)
Тема: The intersection of small balls with a hypersurface in Carnot group and Brownian motion in Carnot group
Тези. We consider a Carnot group and a smooth hypersurface in it. Taking a ball w.r.t. natural distance in Carnot group we study its surface measure w.r.t. the given hypersurface. The estimates of such measure when the radius of the ball is small will be presented. We will also discuss how such estimates are connected to the properties of the corresponding Brownian motion on Carnot group.
- Семінар 17.09.2024
Доповідач: Віталій Конаровський (Гамбурзький університет, Інститут математики НАН України)
Тема: A quantitative central limit theorem for the simple symmetric exclusion process
Тези. We will discuss a quantitative central limit theorem for the simple symmetric exclusion process on a multidimensional discrete torus. Our argument is based on a comparison of the generators of the density fluctuation field of the symmetric exclusion process and the generalized Ornstein-Uhlenbeck process, as well as on an infinite-dimensional Berry-Essen bound for the initial particle fluctuations. The obtained rate of convergence is optimal. It is a joint work with Benjamin Gess.
- Семінар 28.05.2024
Доповідач: Насір Ганіходжаєв (Інститут математики, Ташкент, Узбекістан)
Тема: Phase Diagrams of Lattice Models with Competing Interactions
Тези. The existence of competing interactions lies at the heart of a variety of original phenomena in magnetic systems, ranging from the spin-glass transitions found in many disordered materials to the modulated phases with an infinite number of commensurate regions, that are observed in certain models with periodic interactions. Ising models with competing interactions has recently been considered extensively because of the appearance of nontrivial magnetic orderings. If competing interactions are defined on prolonged second or third nearest-neighbors, i.e. spins belonging to the same branch then corresponding phase diagram is very rich, and if second or third nearest-neighbors belong to different branches of the tree then corresponding phase diagram consists of paramagnetic, ferromagnetic, paramodulated with period p = 2 and anti-ferromagnetic phases. It is shown that for 1-D Ising model with competing interactions one can reach phase transition while for usual 1-D Ising model we don’t reach phase transition.