Related papers: Conditioned random walks from Kac-Moody root syste…

We report on the asymptotic behaviour of a new model of random walk, we term the bindweed model, evolving in a random environment on an infinite multiplexed tree. The term \textit{multiplexed} means that the model can be viewed as a nearest…

This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…

The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the…

We study the asymptotic distribution of random walks on $\mathbb Z^d$ ($d\ge1$) in deterministic reversible environments defined by an assignment of a positive conductance to each edge of $\mathbb Z^d$. We identify a deterministic set of…

This paper explores a conditional Gibbs theorem for a random walkinduced by i.i.d. (X_{1},..,X_{n}) conditioned on an extreme deviation of its sum (S_{1}^{n}=na_{n}) or (S_{1}^{n}>na_{n}) where a_{n}\rightarrow\infty. It is proved that when…

We study variable-speed random walks on $\mathbb Z$ driven by a family of nearest-neighbor time-dependent random conductances $\{a_t(x,x+1)\colon x\in\mathbb Z, t\ge0\}$ whose law is assumed invariant and ergodic under space-time shifts. We…

We consider nearest neighbor weighted random walks on the $d$-dimensional box $[n]^d$ that are governed by some function $g:[0,1] \ra [0,\iy)$, by which we mean that standing at $x$, a neighbor $y$ of $x$ is picked at random and the walk…

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…

We consider random walks on the nonnegative integers in a space-time dependent random environment. We assume that transition probabilities are given by independent $\mathrm{Beta}(\mu,\mu)$ distributed random variables, with a specific…

We consider a special case of random walk in random environment (RWRE) on Z^d where the environment is periodic (RWPE). Under natural conditions, we show that law of large numbers and central limit theorem holds. In the ballistic nearest…

We prove a law of large numbers for a class of $\Z^d$-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called \emph{conditional cone-mixing} and that…

We present a procedure that determines the law of a random walk in an iid random environment as a function of a single "typical" trajectory. We indicate when the trajectory characterizes the law of the environment, and we say how this law…

We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by…

A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

We consider the random Cayley graphs of a sequence of finite nilpotent groups of diverging sizes $G=G(n)$, whose ranks and nilpotency classes are uniformly bounded. For some $k=k(n)$ such that $1\ll\log k \ll \log |G|$, we pick a random set…

We consider one-dependent random walks on $\mathbb{Z}^d$ in random hypergeometric environment for $d\ge 3$. These are memory-one walks in a large class of environments parameterized by positive weights on directed edges and on pairs of…

We consider weighted geodesic random walks in a complete Riemannian manifold $(M,g)$. We show that for almost all sequences of weights (with respect to a suitable measure), these weighted geodesic random walks satisfy, when suitably scaled,…

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step…

We study random walks on metric spaces with contracting isometries. In this first article of the series, we establish sharp deviation inequalities by adapting Gou\"ezel's pivotal time construction. As an application, we establish the…