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## Fluctuations in Markov Processes: Time Symmetry and Martingale Approximation

- S. Olla, C. Landim, T. Komorowski
- Mathematics
- 6 July 2012

iffusive phenomena in statistical mechanics and in other fields arise from markovian modeling and their study requires sophisticated mathematical tools. In infinite dimensional situations, time… Expand

## Kinetic limits for waves in a random medium

- G. Bal, T. Komorowski, L. Ryzhik
- Mathematics
- 1 October 2010

2 Diffusive limit for a particle in a random flow 7 2.1 Diffusion of a particle in a time-dependent random flow . . . . . . . . . . . . . . . . 7 2.1.1 The central limit theorem, purely… Expand

## Limit theorems for additive functionals of a Markov chain

- M. Jara, T. Komorowski, S. Olla
- Mathematics
- 1 September 2008

Consider a Markov chain $\{X_n\}_{n\ge 0}$ with an ergodic probability measure $\pi$. Let $\Psi$ a function on the state space of the chain, with $\alpha$-tails with respect to $\pi$, $\alpha\in… Expand

## Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

- T. Komorowski, A. Walczuk
- Mathematics
- 9 February 2011

## A note on the central limit theorem for two-fold stochastic random walks in a random environment

- T. Komorowski, S. Olla
- Mathematics
- 2003

We consider a class of two-fold stochastic random walks in a random environment. The transition probability is given by an ergodic random fi eld on Zd
with two-fold
stochastic realizations. The… Expand

## On ergodicity of some Markov processes

- T. Komorowski, S. Peszat, T. Szarek
- Mathematics
- 25 October 2008

We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space. In addition, weak- * ergodicity, that is, the weak… Expand

## Asymptotics of the phase of the solutions of the random Schrödinger equation

- G. Bal, T. Komorowski, L. Ryzhik
- Mathematics, Physics
- 2009

We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying then the… Expand

## Asymptotic properties of some Markov operators

- T. Komorowski, J. Tyrcha
- Mathematics
- 1989

## Motion in a Gaussian incompressible flow

- T. Komorowski, G. Papanicolaou
- Mathematics, Physics
- 1 February 1997

where B(t), t > 0 denotes the standard d-dimensional Brownian motion and o 2 is the molecular diffusivity of the medium. 'rhe particle trajectory X(t), t 2 0 is assumed, for simplicity, to start at… Expand

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