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We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of ...
This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, th...
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching rand...
Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, pos...
The paper "Critical Truths About Power Laws" (Science, 335, pp665-666) by MPH Stumpf MPH and MA Porter is commented.
Abstract: For a finite set of points $P$ in $R^d$, the function $d_P:R^d \to R_+$ measures Euclidean distance to the set $P$. We study the number of critical points of $d_P$ when $P$ is random. In par...
Abstract: We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega...
Abstract: The Swendsen-Wang dynamics is a Markov chain widely used by physicists to sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer, Frieze and Rue proved that on the com...
Abstract: We investigate the inhomogeneous Galton--Watson processes with immigration, where $\rho_n$ the offspring means in the $n^\textrm{th}$ generation tends to 1. We show that if the second deriva...
Abstract: We consider a critical branching particle system in $\R^d$, composed of individuals of a finite number of types $i\in\{1,...,K\}$. Each individual of type $i$ moves independently according t...
Consider a critical random multigraph Gn constructed by the con guration model such that its vertex degrees are independent random variables with the same distribution  (criticality means that the se...

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