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Search: authors:"Piotr Miłoś"

3 papers found.
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Spatial Central Limit Theorem for Supercritical Superprocesses

We consider a measure-valued diffusion (i.e., a superprocess). It is determined by a couple \((L,\psi )\), where L is the infinitesimal generator of a strongly recurrent diffusion in \(\mathbb {R}^{d}\) and \(\psi \) is a branching mechanism assumed to be supercritical. Such processes are known, see for example, (Englander and Winter in Ann Inst Henri Poincaré 42(2):171–185, 2006...

Delocalization of Two-Dimensional Random Surfaces with Hard-Core Constraints

We study the fluctuations of random surfaces on a two-dimensional discrete torus. The random surfaces we consider are defined via a nearest-neighbor pair potential, which we require to be twice continuously differentiable on a (possibly infinite) interval and infinity outside of this interval. No convexity assumption is made and we include the case of the so-called hammock...

\(U\) -Statistics of Ornstein–Uhlenbeck Branching Particle System

We consider a branching particle system consisting of particles moving according to the Ornstein–Uhlenbeck process in \(\mathbb {R}^d\) and undergoing a binary, supercritical branching with a constant rate \(\lambda >0\) . This system is known to fulfill a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem (CLT) has...