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A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...
In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile {f(n),n ∈ Z}.One interesting result is that two independen...
We study the asymptotic behaviour of occupation times of a transient random walk in a quenched random environment on a strip in a sub-di usive regime. The asymptotic behaviour of hitting times, whic...
Local Limit Theorems for Random Walks in a 1D Random Environment     RWRE  quenched random environments       font style='font-size:12px;'> 2015/9/29
We consider random walks (RW) in a one-dimensional i.i.d. random environment with jumps to the nearest neighbours. For almost all environments, we prove a quenched Local Limit Theorem (LLT) for the...
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       font style='font-size:12px;'> 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.
We consider excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on the critical case for the transition between rec...
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...
Random Walks on Finite Groups     Finite Groups  Random       font style='font-size:12px;'> 2015/8/26
Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shuffling methods. ...
ON RANDOM WALKS ON WREATH PRODUCTS     PRODUCTS  RANDOM WALKS       font style='font-size:12px;'> 2015/8/26
Wreath products are a type of semidirect product. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks ...
We establish the lower bound p2t (e, e)  exp(−t1/3), for the large times asymptotic behaviours of the probabilities p2t (e, e) of return to the origin at even times 2t, for random walks assoc...
RANDOM WALKS DRIVEN BY LOW MOMENT MEASURES     LOW MOMENT MEASURES  RANDOM WALKS DRIVEN       font style='font-size:12px;'> 2015/8/26
second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function  :G→ [0,+∞], we introduce a function G, which describes the ...
GAUSSIAN ESTIMATES FOR MARKOV CHAINS AND RANDOM WALKS ON GROUPS     GROUPS  MARKOV CHAINS       font style='font-size:12px;'> 2015/8/26
A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular g...
Probability on Groups: Random Walks and Invariant Diffusions     Invariant Diffusions  Random Walks       font style='font-size:12px;'> 2015/8/26
What do card shuffling, volume growth, and Harnack inequalities have to do with each other? They all arise in the study of random walks on groups. Probability on groups is concerned with probabil...
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...

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