Related papers: Statistics of first-passage Brownian functionals
We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long time…
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet…
In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative…
We consider first-passage percolation on $\mathbb{Z}^2$ with i.i.d. weights, whose distribution function satisfies $F(0) = p_c = 1/2$. This is sometimes known as the "critical case" because large clusters of zero-weight edges force passage…
We consider the area functional defined by the integral of an Ornstein-Uhlenbeck process which starts from a given value and ends at the time it first reaches zero (its equilibrium level). Exact results are presented for the mean, variance,…
We consider the movement of a particle advected by a random flow of the form $\vv+\delta \bF(\vx)$, with $\vv\in\R^d$ a constant drift, $\bF(\vx)$ -- the fluctuation -- given by a zero mean, stationary random field and $\delta\ll 1$ so that…
An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
We consider $N$ Brownian motions diffusing independently on a line, starting at $x_0>0$, in the presence of an absorbing target at the origin. The walkers undergo stochastic resetting under two protocols: (A) each walker resets…
Brownian motion in terms of Lifson and Jackson (LJ) formula has been widely explored in periodic systems and it has been believed for a long time that the LJ formula only applies to periodic potentials. Recently we show that for the…
We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position $x_0$ ($>0$). By deriving the exit probability of RBM in an interval $\left[0, M…
Let $\mu_t$ denote the critical derivative Gibbs measure of branching Brownian motion at time $t$. It has been proved by Madaule (Stochastic Process. Appl. 126 (2016), no. 2, 470--502) and Maillard and Zeitouni (Ann. Inst. Henri Poincar\'e…
We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has positive Lebesgue measure with positive…
There exist a large literature on the application of $q$-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, $P_R(0,t)$,…
We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup's functional integral approach, we obtain the…
We compute the joint probability density function (jpdf) P_N(M, \tau_M) of the maximum M and its position \tau_M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N \to \infty, this jpdf is…
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…
We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in particular that its exponential decreasing rate is a…
The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the…
We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches:…