Related papers: Random paths with bounded local time

We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the…

In this paper, we study elastic Brownian motion on a \(C^2\) domain. Instead of being killed at the boundary, the process restarts from a random position inside the domain. We characterize this process through its stochastic differential…

We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time $n$. Assuming that the moment of order $2+\delta$ is…

In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given…

In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…

We consider a random walk in a stationary ergodic environment in $\mathbb Z$, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right…

Let $n$ particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stay inside a Weyl chamber; the Weyl group for this…

In this article, we study the maximal displacement in a branching random walk. We prove that its asymptotic behaviour consists in a first almost sure ballistic term, a negative logarithmic correction in probability and stochastically…

We consider the random walk of a particle in a two-dimensional self-affine random potential of Hurst exponent $H=1/2$ in the presence of an external force $F$. We present numerical results on the statistics of first-passage times that…

Let \alpha ([0,1]^p) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log P\bigl{\alpha([0,1]^p)\ge…

We study the strong form of the ballistic conjecture for random walks in random environments (RWRE). This conjecture asserts that any RWRE which is directionally transient for a nonempty open set of directions satisfies condition $(T)$…

We consider a random walk on the support of an ergodic simple point process on R^d, d>1, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a…

The mean-squared displacement (MSD) is an averaged quantity widely used to assess anomalous diffusion. In many cases, such as molecular motors with finite processivity, dynamics of the system of interest produce trajectories of varying…

The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…

We consider a biased nearest-neighbor random walk on $\Z$ which at each step is trapped for some random time with random, site-dependent mean. We derive a simple formula for the speed function in terms of the model parameters.

We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the…

For a random walk in an elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying the a ballisticity condition slightly weaker than condition (T'), We consider the probability of linear slowdown. We show an…

We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential $V(x)=\mu |x-x_0|$, where $\mu>0$ is the strength of the potential and $x_0>0$ is the…

We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive…

We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the…