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We study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the…
Research on the similarity of a graph to being a tree - called the treewidth of the graph - has seen an enormous rise within the last decade, but a practically fast algorithm for this task has been discovered only recently by Tamaki (ESA…
We propose a general strategy for solving nonlinear integro-differential evolution problems with periodic boundary conditions, where no direct maximum/minimum principle is available. This is motivated by the study of recent macroscopic…
Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
We consider a reaction-diffusion system of densities of two types of particles, introduced by Edouard Hannezo et al. in the context of branching morphogenesis. It is a simple model for a growth process: active, branching particles form the…
We introduce a one-dimensional quasiperiodic mosaic model with analytically solvable mobility edges that exhibit different phase transitions depending on the system parameters. Specifically, by combining mosaic quasiperiodic…
The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for…
Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the…
In this note, we recall the definition of the binary branching model with Moran type interactions (BBMMI) introduced in [8]. In this interacting particle system, particles evolve, reproduce and die independently and, with a probability that…
Let $[\mathcal{P}]$ be the points of a Poisson process on $\mathbb{R}^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set…
Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to…
We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace transform of the stationary distribution…
In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares Sales, Reed and Thomass\'e, we prove that every oriented graph with all in- and out-degrees greater than 5k/8 contains an alternating path of length k. This…
We present a diffusion model of surface soil pollution from a stationary source based on the symmetric stochastic motion at finite speed in the plane $\Bbb R^2$, also called the planar Markov random flight, whose lifetime is a random…
We develop a method of stochastic differential equation to simulate electron acceleration at astrophysical shocks. Our method is based on It\^{o}'s stochastic differential equations coupled with a particle splitting, employing a skew…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
Consider an multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this…