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Random Point Processes and Clustering in Interacting Particle Systems

Vladimir Fomichov (National Technical University of Ukraine)
Stochastics Seminar
Monday, 13 May, 2019, at 13:15-14:00, in Aud. G1 (1532-116)
In our talk we will consider systems of interacting one-dimensional Brownian particles.

Firstly, we will discuss the random point processes formed by the clusters in systems with coalescence and, basing on recent work of R. Tribe and O. Zaboronski, show that they belong to a class generalising determinantal point processes. In addition, we will prove the central limit theorem for the number of clusters in an interval when the length of this interval tends to infinity.

Secondly, we will discuss the concentration of measure in diffeomorphic stochastic flows that approximate coalescing particle systems. In particular, the high-level exceedances of the stationary processes formed by the corresponding densities will be studied. More precisely, using the Rice formula, we will compute the level-crossing intensity of these processes and establish its asymptotic behaviour as the height of the level tends to infinity.

Organised by: math
Contact person: Jevgenijs Ivanovs