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山西大同大学概率论与数理统计课件第五章 大数定律与中心极限定理。
中国科学技术大学2014年硕士学位研究生入学考试高等数学B试题。
黑龙江大学2016年攻读硕士学位研究生自命题数学二初试考试大纲。
LIMIT THEOREMS FOR DISPERSING BILLIARDS WITH CUSPS
Dispersing billiards Sinai billiards cusps
2015/9/29
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statisti...
CENTRAL LIMIT THEOREM FOR RECURRENT RANDOM WALKS ON A STRIP WITH BOUNDED POTENTIAL
RANDOM WALKS CENTRAL LIMIT THEOREM
2015/9/29
We prove that a recurrent random walk (RW) in i.i.d. random
environment (RE) on a strip which does not obey the Sinai law exhibits the
Central Limit asymptotic behaviour.
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...
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...
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 ...
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...