Related papers: Some aspects of additive coalescents
We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a…
We propose a path transformation which applied to a cyclically exchangeable increment process conditions its minimum to belong to a given interval. This path transformation is then applied to processes with start and end at zero. It is seen…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
While a drop of liquid is placed on another liquid surface, two possible coalescence outcomes are observed. The parent drop bounces several times, floats and then disappears within the liquid pool without producing daughter droplets. This…
We study boundary traces of shift-invariant diffusions: two-dimensional diffusions in the upper half-plane $\mathbb{R} \times [0, \infty)$ (or in $\mathbb{R} \times [0, R)$) invariant under horizontal translations. We prove that the…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
Amplified spontaneous emission is a common noise source in active optical systems, it is generally seen as being an incoherent process. Here we excite an ensemble of rare earth ion dopants in a solid with a {\pi}-pulse, resulting in…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective…
We investigate the typical sizes and shapes of sets of points obtained by irregularly tracking two-dimensional Brownian bridges. The tracking process consists of observing the path location at the arrival times of a non-homogeneous Poisson…
This article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and L\'evy processes which summarize and extend the literature on these subjects. The results surveyed include point…
Using an electrical method and high-speed imaging we probe drop coalescence down to 10 ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that at sufficiently low approach velocity where deformation is…
We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.
Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents $q\nu(q)$ by measuring the absolute $q$-th moment $\langle |x|^q\rangle$.…
Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a…
Among the topics we discuss are certain joint densities (for sides and for angles), acuteness probabilities and bivariate Rice moments.
We explore the connection between tasep-like interacting particle systems and last passage percolation type polymer models, focusing on three models: Geometric, Exponential and Brownian last passage percolation and their associated tasep…
We design exact polynomial expansions of a class of Feynman--Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
Random increasing k-trees represent an interesting, useful class of strongly dependent graphs for which analytic-combinatorial tools can be successfully applied. We study in this paper a notion called connectivity-profile and derive…