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SCALING LIMITS OF RECURRENT EXCITED RANDOM WALKS ON INTEGERS
Limit random walk RECURRENT EXCITED
2015/9/29
We describe scaling limits of recurrent excited random walks (ERWs) on
Z in i.i.d. cookie environments with a bounded number of cookies per site. We allow
both positive and negative excitations.
Central Limit Theorem for Excited Random Walk in the Recurrent Regime
Recurrent Regime Excited Random Walk
2015/9/29
We consider excited random walk on a strip. We assume that the
cookies are positive and that the total expected drift per site is less than 1/L where
L is the width of the strip. We prove a quenched...
QUENCHED LIMIT THEOREMS FOR NEAREST NEIGHBOUR RANDOM WALKS IN 1D RANDOM ENVIRONMENT
NEIGHBOUR RANDOM WALKS IMIT THEOREMS
2015/9/29
It is well known that random walks in one dimensional random environment can exhibit subdiffusive behavior due
to presence of traps. In this paper we show that the passage times
of diffe...
A LOCAL LIMIT THEOREM FOR SUMS OF INDEPENDENT RANDOM VECTORS
THEOREM FOR SUMS INDEPENDENT RANDOM
2015/9/29
We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
In other words where is the boundary between truly random and
almost deterministic behavior? I believe that very little randomness
is needed. For example consider the following model. Let f1 : : : f...
One of the surprising discoveries of dynamical systems theory is
that many deterministic systems with non-zero Lyapunov exponents
satisfy the same limit theorems as the sums of independent random
v...
ANOMALOUS CURRENT IN PERIODIC LORENTZ GASES WITH INFINITE HORIZON
PERIODIC LORENTZ GASES INFINITE HORIZON
2015/9/29
We study electrical current in two-dimensional periodic Lorentz gas in the presence of a weak homogeneous etric field.When the horizon is finite, i.e. the free flights between
colli...
PRELUDE TO A KISS
KISS limit
2015/9/29
We consider expanding maps of the circle with an almost neutral fixed point
c. In this setting the ergodic averages of a smooth observable A satisfy the Central Limit
Theorem. If A(c) = 0 we s...
We consider a stochastic flow driven by a finite-dimensional Brownian
motion. We show that almost every realization of such a flow exhibits strong
statistical properties such as th...
We consider the evolution of a connected set in Euclidean space
carried by a periodic incompressible stochastic
ow. While for almost every
realization of the random
ow at time t most of the part...
A Limit Shape Theorem for Periodic Stochastic Dispersion
Periodic Stochastic Dispersion Shape
2015/9/29
We consider the evolution of a connected set on the plane carried by a space
periodic incompressible stochastic flow. While for almost every realization of
the stochastic flow at time t ...
EVOLUTION OF ADIABATIC INVARIANTS IN STOCHASTIC AVERAGING
STOCHASTIC AVERAGING ADIABATIC INVARIANTS
2015/9/29
An averaging problem with Markov fast motion is
considered. The di usive limit is obtained for the evolution of adabatic invariants under the assumption that the averaged motion
is ergodic on almost...
LIMIT THEOREMS FOR LOCALLY PERTURBED PLANAR LORENTZ PROCESSES
LOCALLY PERTURBED PLANAR PROCESSES
2015/9/29
Modify the scatterer conguration of a planar, nitehorizon Lorentz process in a bounded domain. Sinai asked in
1981 whether for the diffusively scaled variant of the modied
process convergence to Bro...
NON EQUILIBRIUM DENSITY PROFILES IN LORENTZ TUBES WITH THERMOSTATED BOUNDARIES
EQUILIBRIUM DENSITY PROFILES THERMOSTATED BOUNDARIES
2015/9/29
We consider a long Lorentz tube with absorbing boundaries.
Particles are injected to the tube from the left end. We compute the equilibrium density pro les in two cases: the semi-in nite tube (in whi...
We study a particle moving in R
2 under a constant (external) force
and bouncing off a periodic array of convex domains (scatterers); the
latter must satisfy a standard ‘finite horizon’...