Related papers: Exact mean first-passage time on the T-graph

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The…

In the models of first-passage percolation and directed first-passage percolation on $\mathbb{Z}^d$, we consider a family of i.i.d. random variables indexed by the set of edges of the graph, called passage times. For every vertex $x \in…

Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…

Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…

In this paper, following the paper ``On the average hitting times of the squares of cycles,'' we provide an explicit formula for the average hitting times of a simple random walk on a directed graph with $N$ vertices, where the graph…

The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…

In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based on a dimensionality reduction technique for Markov State Models, known as local-equilibrium (LE). We show that for a…

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean…

We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position,…

Let (Xt, t >= 0) be a diffusion process with jumps, sum of a Brownian motion with drift and a compound Poisson process. We consider T_x the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of T_x has a…

A simple lemma bounds $\mathrm{s.d.}(T)/\mathbb{E} T$ for hitting times $T$ in Markov chains with a certain strong monotonicity property. We show how this lemma may be applied to several increasing set-valued processes. Our main result…

We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…

Certain biological reactions, such as receptor-ligand binding at cell-cell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T cell interface, a…

We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…

We study the edge-averaging process on a finite, connected graph $G = (V, E)$. Initially, the vertices in $V$ are endowed with i.i.d.\ real-valued opinions $(f_0(v))_{v \in V}$. Edges are activated according to i.i.d.\ Poisson clocks of…

In this paper we analyse random walk on a fractal structure, specifi- cally fractal curves, using the recently develped calculus for fractal curves. We consider only unbiased random walk on the fractal stucture and find out the…

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 first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…

In 1999, Zhang proved that, for first passage percolation on the square lattice $\mathbb{Z}^2$ with i.i.d. non-negative edge weights, if the probability that the passage time distribution of an edge $P(t_e = 0) =1/2 $, the critical value…