### Malliavin calculus and its Applications

Head of the seminar: Professor Andrey A. Dorogovtsev

17.00, room 208.

Secretary of the seminar: Georgii Riabov

- Seminar 05.11.2024
Speaker:

**Kyrylo Kuchynskyi**(Institute of Mathematics of NAS of Ukraine)Topic:

**Asymptotic behavior of the solution to the multi-dimensional stochastic differential equation with interactions** - Seminar 29.10.2024
Speaker:

**Mykola Portenko**(Institute of Mathematics of NAS of Ukraine)Topic:

**On the killing coefficient of multidimensional Brownian motion killed at the hitting time of a given hypersurface** - Seminar 22.10.2024
Speaker:

**Andrey A. Dorogovtsev**(Institute of Mathematics of NAS of Ukraine, joint work with Naoufel Salhi, University of Kairouan)Topic:

**Universal generalized functionals** - Seminar 08.10.2024
Speaker:

**Mykola Vovchanskii**(Institute of Mathematics of NAS of Ukraine)Topic:

**On multidimensional point densities for Arratia flows with drift** - Seminar 01.10.2024
Speaker:

**Vadym Radchenko**(Taras Shevchenko National University of Kyiv)Topic:

**Equations with a symmetric integral with respect to stochastic measures**Abstract.

*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.* - Seminar 24.09.2024
Speaker:

**Oleksii Rudenko**(Institute of Mathematics of NAS of Ukraine)Topic:

**The intersection of small balls with a hypersurface in Carnot group and Brownian motion in Carnot group**Abstract.

*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.* - Seminar 17.09.2024
Speaker:

**Vitalii Konarovskyi**(University of Hamburg, Institute of Mathematics of NAS of Ukraine)Topic:

**A quantitative central limit theorem for the simple symmetric exclusion process**Abstract.

*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.* - Seminar 28.05.2024
Speaker:

**Nasir Ganikhodjaev**(Institute of Mathematics, Tashkent, Uzbekistan)Topic:

**Phase Diagrams of Lattice Models with Competing Interactions**Abstract.

*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.* - Seminar 14.05.2024
Speaker:

**Andrea Ottolini**(University of Washington)Topic:

**Hitting times in random graphs**Abstract.

*I will discuss a general approach to derive nearly-exact formulas for average hitting times in large graphs. As a main example, we will consider the case of the stochastic block model with two communities, though the idea is much more general. Time permitting, I will explain the connection with community detection.* - Seminar 30.04.2024
Speaker:

**Kateryna Hlyniana**(Institute of Mathematics of NAS of Ukraine)Topic:

**Filtration problem for SDE with interaction**