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SCALING LIMITS OF RECURRENT EXCITED RANDOM WALKS ON INTEGERS
Limit random walk RECURRENT EXCITED
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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
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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
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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
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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...
SAMPLE PATH PROPERIES OF RANDOM TRANSFORMATIONS
TRANSFORMATIONS SAMPLE PATH PROPERIES
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2015/9/29
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...
Limit theorems for toral translations
toral translations Limit
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2015/9/29
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
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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
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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...
SAMPLE PATH PROPERTIES OF THE STOCHASTIC FLOWS
STOCHASTIC FLOWS PATH PROPERTIES
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2015/9/29
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...
HAUSDORFF DIMENSION IN STOCHASTIC DISPERSION
STOCHASTIC DISPERSION HAUSDORFF DIMENSION
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2015/9/29
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
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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
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2015/9/29
An averaging problem with Markov fast motion is
considered. The diusive 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
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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
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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 proles in two cases: the semi-innite tube (in whi...
Galton Board: limit theorems and recurrence
limit theorems recurrence
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2015/9/29
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’...