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We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on…

Probability · Mathematics 2018-01-08 Idan Alter , Gideon Amir

In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…

Probability · Mathematics 2022-12-06 Maxime Hauray , Etienne Pardoux , Yen V. Vuong

When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…

Soft Condensed Matter · Physics 2022-05-26 Vipul Vijigiri , Cedric Courbon , Guillaume Kermouche , Juliette Cayer-Barrioz

We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge,…

Statistical Mechanics · Physics 2021-04-22 Gesualdo Delfino , Marianna Sorba , Alessio Squarcini

We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…

Probability · Mathematics 2016-06-07 Antonio Di Crescenzo , Barbara Martinucci , Abdelaziz Rhandi

This paper studies a multiclass spatial birth-and-death (SBD) processes on a compact region of the Euclidean plane modeling wireless interactions. In this model, users arrive at a constant rate and leave at a rate function of the…

Probability · Mathematics 2023-01-20 Pierre Popineau , François Baccelli

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…

Analysis of PDEs · Mathematics 2023-06-13 Marie Doumic , Sophie Hecht , Benoit Perthame , Diane Peurichard

We introduce a multitype contact process with temporal heterogeneity involving two species competing for space on the $d$-dimensional integer lattice. Time is divided into seasons called alternately season 1 and season 2. We prove that…

Probability · Mathematics 2009-10-22 B. Chan , R. Durrett , N. Lanchier

We consider one-dimensional biased voter models, where 1's replace 0's at a faster rate than the other way round, started in a Heaviside initial state describing the interface between two infinite populations of 0's and 1's. In the limit of…

Probability · Mathematics 2020-07-30 Rongfeng Sun , Jan M. Swart , Jinjiong Yu

In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…

Probability · Mathematics 2024-11-14 Dirk Erhard , Tertuliano Franco , Milton Jara , Eduardo Pimenta

Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…

Probability · Mathematics 2015-08-27 Kevin Kuoch

The irreversible growth of a binary mixture under far-from-equilibrium conditions is studied in three-dimensional confined geometries of size $L_x \times L_y \times L_z$, where $L_z \gg L_x = L_y$ is the growing direction. A competing…

Statistical Mechanics · Physics 2009-11-11 Julián Candia , Ezequiel V. Albano

Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…

Populations and Evolution · Quantitative Biology 2025-01-14 Jordi Piñero , S. Redner , Ricard Solé

The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity $v$, which increases as $v \sim (F-F_c)^\theta$ for…

Condensed Matter · Physics 2009-10-28 Heiko Leschhorn , Thomas Nattermann , Semjon Stepanow , Lei-Han Tang

We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate $1$. Particles of type 1 can occupy any…

Probability · Mathematics 2019-07-31 Mariela Pentón Machado

We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…

Analysis of PDEs · Mathematics 2021-09-28 Chiara Giverso , Tommaso Lorenzi , Luigi Preziosi

This paper is concerned with a natural variant of the contact process modeling the spread of knowledge on the integer lattice. Each site is characterized by its knowledge, measured by a real number ranging from 0 = ignorant to 1 =…

Probability · Mathematics 2025-03-24 Nicolas Lanchier , Max Mercer , Hyunsik Yun

This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…

Probability · Mathematics 2015-08-14 Nicolas Champagnat , Denis Villemonais

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…

Probability · Mathematics 2007-05-23 Thomas M. Liggett , Rinaldo B. Schinazi , Jason Schweinsberg

The translational motion of a solid sphere near a deformable fluid interface is studied in the low Reynolds number regime. In this problem, the fluid flow driven by the sphere is dynamically coupled the instantaneous conformation of the…

Soft Condensed Matter · Physics 2010-04-26 Thomas Bickel