相关论文: Random Walk in a Random Environment and First-Pass…

In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation…

We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect…

Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…

We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [6]. We describe our results…

Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…

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…

We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk…

We study how the recurrence and transience of space-time sets for a branching random walk on a graph depends on the offspring distribution. Here, we say that a space-time set $A$ is recurrent if it is visited infinitely often almost surely…

We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the…

We consider one infinite path of a Random Walk in Random Environment (RWRE, for short) in an unknown environment. This environment consists of either i.i.d.\ site or bond randomness. At each position the random walker stops and tells us the…

We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a…

We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process.…

We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous…

We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…

This paper studies the behavior of RWRE on trees in the critical case left open in previous work. For trees of exponential growth, a random perturbation of the transition probabilities can change a transient random walk into a recurrent…

We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight…

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average…

We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…