Related papers: Limit laws for transient random walks in random en…

Let $(S_n)_{n \geq 0}$ be a transient random walk in the domain of attraction of a stable law and let $(\xi(s))_{s \in \mathbb{Z}}$ be a stationary sequence of random variables. In a previous work, under conditions of type $D(u_n)$ and…

In this paper, we are interested in the asymptotic behaviour of the sequence of processes $(W_n(s,t))_{s,t\in[0,1]}$ with \begin{equation*} W_n(s,t):=\sum_{k=1}^{\lfloor nt\rfloor}\big(1_{\{\xi_{S_k}\leq s\}}-s\big) \end{equation*} where…

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…

Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $\alpha\in[0,\infty)$ and let $L_n(\alpha)$ be the spatial sum of the $\alpha$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range,…

Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…

In recent years, there has been an interest in deriving certain important probabilistic results as consequences of deterministic ones; see for instance \cite{beig} and \cite{acc}. In this work, we continue on this path by deducing a well…

For a continuous-time random walk $X=\{X_t,t\ge 0\}$ (in general non-Markov), we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X_s)ds$, $t\ge 0$. Similarly to the Markov…

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 show that random walk in uniformly elliptic i.i.d. environment in dimension $\geq5$ has at most one non zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes…

We study the random walk in random environment on {0,1,2,...}, where the environment is subject to a vanishing (random) perturbation. The two particular cases we consider are: (i) random walk in random environment perturbed from Sinai's…

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…

We study random walk with unbounded jumps in random environment. The environment is stationary and ergodic, uniformly elliptic and decays polynomially with speed $Dj^{-(3+\varepsilon_0)}$ for some small $\varepsilon_0>0$ and proper $D>0.$…

We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\"ollering, 2016] and prove a…

A transient stochastic process is considered strongly transient if conditioned on returning to the starting location, the expected time it takes to return the the starting location is finite. We characterize strong transience for a…

We consider a random walk with a negative drift and with a jump distribution which under Cram\'er's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably…

Random walks in random scenery are processes defined by $$Z_n:=\sum_{k=1}^n\omega_{S_k}$$ where $S:=(S_k,k\ge 0)$ is a random walk evolving in $\mathbb{Z}^d$ and $\omega:=(\omega_x, x\in{\mathbb Z}^d)$ is a sequence of i.i.d. real random…

We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose…

In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in…

We consider $d$ random walks $\big(S_n^{(j)}\big)_{n\in\mathbb{N}}$, $1\leq j \leq d$, in the same random environment $\omega$ in $\mathbb{Z}$, and a recurrent simple random walk $(Z_n)_{n\in\mathbb{N}}$ on $\mathbb{Z}$. We assume that,…