[图书][B] Fluctuations in Markov processes: time symmetry and martingale approximation
The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …
central limit theorems. Using the time symmetry properties of the Markov processes, the …
Quenched invariance principles for walks on clusters of percolation or among random conductances
V Sidoravicius, AS Sznitman - Probability theory and related fields, 2004 - Springer
In this work we principally study random walk on the supercritical infinite cluster for bond
percolation on ℤ d. We prove a quenched functional central limit theorem for the walk when …
percolation on ℤ d. We prove a quenched functional central limit theorem for the walk when …
Invariance principle for the random conductance model
We study a continuous time random walk X in an environment of iid random conductances e
∈ 0, ∞) in Z^ d. We assume that P (e> 0)> p_c, so that the bonds with strictly positive …
∈ 0, ∞) in Z^ d. We assume that P (e> 0)> p_c, so that the bonds with strictly positive …
Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters
P Dario, C Gu - 2021 - projecteuclid.org
We study the heat kernel and the Green's function on the infinite supercritical percolation
cluster in dimension d≥ 2 and prove a quantitative homogenization theorem for these …
cluster in dimension d≥ 2 and prove a quantitative homogenization theorem for these …
Diffusion in turbulence
A Fannjiang, G Papanicolaou - Probability Theory and Related Fields, 1996 - Springer
We prove long time diffusive behavior (homogenization) for convection-diffusion in a
turbulent flow that it incompressible and has a stationary and square integrable stream …
turbulent flow that it incompressible and has a stationary and square integrable stream …
The Gaussian free-field as a stream function: asymptotics of effective diffusivity in infra-red cut-off
G Chatzigeorgiou, P Morfe, F Otto, L Wang - arXiv preprint arXiv …, 2022 - arxiv.org
We analyze the large-time asymptotics of a passive tracer with drift equal to the curl of the
Gaussian free field in two dimensions with ultra-violet cut-off at scale unity. We prove that the …
Gaussian free field in two dimensions with ultra-violet cut-off at scale unity. We prove that the …
Variance decay for functionals of the environment viewed by the particle
JC Mourrat - Annales de l'IHP Probabilités et statistiques, 2011 - numdam.org
For the random walk among random conductances, we prove that the environment viewed
by the particle converges to equilibrium polynomially fast in the variance sense, our main …
by the particle converges to equilibrium polynomially fast in the variance sense, our main …
Infinite-dimensional stochastic differential equations and tail -fields
H Osada, H Tanemura - Probability Theory and Related Fields, 2020 - Springer
We present general theorems solving the long-standing problem of the existence and
pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential …
pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential …
Convection–diffusion equation with space–time ergodic random flow
We prove the homogenization of convection-diffusion in a time-dependent, ergodic,
incompressible random flow which has a bounded stream matrix and a constant mean drift …
incompressible random flow which has a bounded stream matrix and a constant mean drift …
An invariance principle for isotropic diffusions in random environment
AS Sznitman, O Zeitouni - Inventiones mathematicae, 2006 - Springer
We investigate in this work the asymptotic behavior of isotropic diffusions in random
environment that are small perturbations of Brownian motion. When the space dimension is …
environment that are small perturbations of Brownian motion. When the space dimension is …