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We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitti...
We consider the interlacement Poisson point process on the space of doubly-infinite Zd-valued trajectories modulo time shift, tending to infinity at positive and negative infinite times. The set of v...
I declare that I have authored this thesis independently, that I have not used other than the declared sources/resources, and that I have explicitely marked all material which has been quotes either l...
In [Ka], Kaimanovich de ned an augmented rooted tree X for the d-dimensional Sierpinski gasket K. Let fZtg be the simple random walk on X,starting at the root ;.
We study the area distribution of closed walks of length n, begin-ning and ending at the origin. The concept of area of a walk in the square lattice is generalized and the usefulness of the new concep...
Poisson--Dirichlet branching random walks      Poisson--Dirichlet  random walks        font style='font-size:12px;'> 2011/1/20
We determine, to within O(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (v1; v2; : : :) where each vj is the su...
We study generalized branching random walks, which allow time dependence and local dependence between siblings. Under appropriate tail assumptions, we prove the tightness of Fn(· −Med(Fn)), whe...
We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance pr...
Random walks, Kleinian groups, and bifurcation currents     Random walks  Kleinian groups  bifurcation currents       font style='font-size:12px;'> 2010/11/11
Let (\rho_\lambda)_{\lambda\in \Lambda} be a holomorphic family of representations of a finitely generated group G into PSL(2,C), parameterized by a complex manifold \Lambda . We define a notion of b...
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providin...
The asymptotics of the probability that the self-intersection local time of a random walk on $\Z^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some ...
We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform elliptic...
Quantum Random Walks of Waves     Quantum Random  Walks of Waves       font style='font-size:12px;'> 2010/11/8
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part ...
Quantum random walks (QRWs) can be used to perform both quantum simulations and quantum algorithms. In order to exploit this potential, quantum walks on different types of graphs must be physically im...
Consider a system of particles evolving as independent and iden-tically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity ~v, the c...

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