Related papers: Birth-death dynamics for sampling: Global converge…
We consider continuous-time birth-and-death dynamics in $\mathbb{R}^d$ that admit at least one infinite-volume Gibbs point process based on area interactions as a reversible measure. For a large class of starting measures, we show that the…
We deal with two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and…
A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb{R}^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $mu$…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte…
In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of…
We develop a rigorous and implementable framework for Gibbs sampling of infinite-dimensional quantum systems governed by unbounded Hamiltonians. Extending dissipative Gibbs samplers beyond finite dimensions raises fundamental obstacles,…
Continuum Glauber dynamics is a spatial birth-death process whose stationary distribution is a Gibbs distribution. We establish a spectral gap for Continuum Glauber dynamics applied to Gibbs point processes with repulsive pair potentials, a…
This paper is devoted to the construction and study of an equilibrium Glauber-type dynamics of infinite continuous particle systems. This dynamics is a special case of a spatial birth and death process. On the space $\Gamma$ of all locally…
The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…
We show that some classes of birth-and-death processes in continuum (Glauber dynamics) may be derived as a scaling limit of a dynamics of interacting hopping particles (Kawasaki dynamics)
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…
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…
In this paper, we consider a generalized birth-death process (GBDP) and examined its linear versions. Using its transition probabilities, we obtain the system of differential equations that governs its state probabilities. The distribution…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…
The paper studies the counting process arising as a subset of births and deaths in a birth--death process on a finite state space. Whenever a birth or death occurs, the process is incremented or not depending on the outcome of an…
We construct two types of equilibrium dynamics of an infinite particle system in a locally compact metric space $X$ for which a permanental point process is a symmetrizing, and hence invariant measure. The Glauber dynamics is a…