Browsing by Subject "math.PR"
Now showing items 120 of 31

A MergeSplit Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans
We describe a Markov chain on redistricting plans that makes relatively global moves. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts ... 
A stochastic version of Stein Variational Gradient Descent for efficient sampling
We propose in this work RBMSVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply ... 
A Variation on the DonskerVaradhan Inequality for the Principial Eigenvalue
(20170423)The purpose of this short note is to give a variation on the classical DonskerVaradhan inequality, which bounds the first eigenvalue of a secondorder elliptic operator on a bounded domain $\Omega$ by the largest mean first ... 
Asymptotic behavior of branching diffusion processes in periodic media
We study the asymptotic behavior of branching diffusion processes in periodic media. For a supercritical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, ... 
Asymptotic behavior of the Brownian frog model
We introduce an extension of the frog model to Euclidean space and prove properties for the spread of active particles. The new geometry introduces a phase transition that does not occur for the frog model on the lattice. ... 
Complexity of randomized algorithms for underdamped Langevin dynamics
We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst $L^2$ strong error is of order $\Omega(\sqrt{d}\, N^{3/2})$, ... 
Coupling and Decoupling to bound an approximating Markov Chain
(20170727)This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple ... 
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
(20171130)We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the wellknown LennardJones type, and show that the system converges to the unique invariant Gibbs measure ... 
Error bounds for Approximations of Markov chains
(20171130)The first part of this article gives error bounds for approximations of Markov kernels under FosterLyapunov conditions. The basic idea is that when both the approximating kernel and the original kernel satisfy a FosterLyapunov ... 
Fractional stochastic differential equations satisfying fluctuationdissipation theorem
(20170423)We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are nonnegligible. As a result of the fluctuationdissipation theorem, the differential ... 
Geometric ergodicity of Langevin dynamics with Coulomb interactions
This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and ... 
Higher order asymptotics for large deviations  Part I
For sequences of nonlattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit ... 
Higher order asymptotics for large deviations  Part II
We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly dependent increments. As a key example, we show that additive functionals of solutions ... 
Learning interacting particle systems: diffusion parameter estimation for aggregation equations
(20180214)In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to approximate the ... 
Limiting Behaviors of High Dimensional Stochastic Spin Ensemble
Lattice spin models in statistical physics are used to understand magnetism. Their Hamiltonians are a discrete form of a version of a Dirichlet energy, signifying a relationship to the Harmonic map heat flow equation. The ... 
Moderate Deviation for Random Elliptic PDEs with Small Noise
(20170423)Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform ... 
MultiScale MergeSplit Markov Chain Monte Carlo for Redistricting
We develop a MultiScale MergeSplit Markov chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing ... 
Multiscale integrators for stochastic differential equations and irreversible Langevin samplers
(20170423)We study multiscale integrator numerical schemes for a class of stiff stochastic differential equations (SDEs). We consider multiscale SDEs that behave as diffusions on graphs as the stiffness parameter goes to its limit. ... 
Nonlocal SPDE limits of spatiallycorrelatednoise driven spin systems derived to sample a canonical distribution
We study the macroscopic behavior of a stochastic spin ensemble driven by a discrete Markov jump process motivated by the MetropolisHastings algorithm where the proposal is made with spatially correlated (colored) noise, ... 
Nonreversible Markov chain Monte Carlo for sampling of districting maps
Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble of districting plans which are drawn from a prescribed probability distribution that adheres to a realistic ...