Related papers: Duality for spatially interacting Fleming-Viot pro…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
We consider a dual model of decision making, in which an individual forms its opinion based on contrasting mechanisms of imitation and rational calculation. The decision making model (DMM) implements imitating behavior by means of a network…
We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…
We raise a question on whether a dynamical system driven by Markov process is Markovian, for which we are able to propose a criterion and examples of positive case. This investigation leads us to develop (i) a general construction of…
The Fleming-Viot process describes a system of $N$ particles diffusing on a graph with an absorbing site. Whenever one of the particles is absorbed, it is replaced by a new particle at the position of one of the $N-1$ remaining particles.…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…
We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on…
We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate.…
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…