Related papers: Precise large deviations of the first passage time
We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times \{1, \cdots, k\},$ namely the slab $\mathbb{S}_k$ of width $k$. Each edge is assigned independently a passage time of either 0 (with probability $p_c(\mathbb{S}_k)$)…
Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ taking the steps $(1,0)$, $(-1,1)$ and $(0,-1)$ with probabilities $\lambda < (\mu_1\neq \mu_2)$; in particular, $X$ is assumed stable. Let $\tau_n$ be the first time $X$ hits…
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two-…
We investigate the first-passage properties of a jump process with a constant drift, focusing on two key observables: the first-passage time $\tau$ and the number of jumps $n$ before the first-passage event. By mapping the problem onto an…
We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is…
We consider the mean first passage time of a random walker moving in a potential landscape on a finite interval, starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
Let $\varepsilon>0$ and, for an odd prime $p$, set $$ S_\ell(p):=\sum_{n\le \ell}\left(\frac{n}{p}\right). $$ Define the first-passage time $$ f_\varepsilon(p):=\min\{\ell\ge 1:\ S_\ell(p)<\varepsilon\ell\}. $$ We prove that there exists a…
We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which…
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial…
We consider a run-and-tumble particle (RTP) in one dimension, subjected to a telegraphic noise with a constant rate $\gamma$, and in the presence of an external confining potential $V(x) = \alpha |x|^p$ with $p \geq 1$. We compute the mean…
In this contribution we are concerned with the asymptotic behaviour as $u\to \infty$ of $\mathbb{P}\{\sup_{t\in [0,T]} X_u(t)> u\}$, where $X_u(t),t\in [0,T],u>0$ is a family of centered Gaussian processes with continuous trajectories. A…
We derive a Sturm-Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener-Hopf integral equation obtained from the theory of…
We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem…
We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is the trace of the (i - 1)-st walk. The sequence of bias vectors…
The concept of a mean first passage time is used to study the time lapse over which a fissioning system may emit light particles. The influence of the "transient" and "saddle to scission times" on this emission are critically examined. It…
In this note we consider the time of the collision $\tau$ for $n$ independent Brownian motions $X^1_t,...,X_t^n$ with drifts $a_1,...,a_n$, each starting from $x=(x_1,...,x_n)$, where $x_1<...<x_n$. We show the exact asymptotics of…
Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional brownian motion in an…
We study the random walk problem on a class of deterministic Scale-Free networks displaying a degree sequence for hubs scaling as a power law with an exponent $\gamma=\log 3/\log2$. We find exact results concerning different first-passage…
First passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We…