Related papers: First-detection-time statistics in many-body quant…
We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with diffusion coefficient $D$ that starts at the origin and reaches $X$ either: (i) at time $T$ or (ii) for the first time at time $T$. We…
In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study…
The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one…
We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
The waiting time distribution $w(\tau)$, i.e. the probability for a delay $\tau$ between two subsequent transition (`jumps') of particles, is a statistical tool in (quantum) transport. Using generalized Master equations for systems coupled…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
The amount $Q$ of particles that are transported via a path of motion is characterized by its expectation value $<Q>$ and by its variance $Var(Q)$. We analyze what happens if a particle has two optional paths available to get from one site…
The distribution of the first-passage time (FPT)$T_a$ for a Brownian particle with drift $\mu$ subject to hitting an absorber at a level $a>0$ is well-known and given by its density $\gamma(t) = \frac{a}{\sqrt{2 \pi t^3} } e^{-\frac{(a-\mu…
Quantized systems whose underlying classical dynamics possess an elaborate mixture of regular and chaotic motion can exhibit rather subtle long-time quantum transport phenomena. In a short wavelength regime where semiclassical theories are…
Mobile sensing enabled by GPS or smart phones has become an increasingly important source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a reasonable penetration rate of probe vehicles. From the…
We study quantum walks of many non-interacting particles on a beam splitter array, as a paradigmatic testing ground for the competition of single- and many-particle interference in a multi-mode system. We derive a general expression for…
The dynamics of a particle propagating in free space is described by its position and momentum, where quantum mechanics prohibits the simultaneous identification of two non-commutative physical quantities. Recently, a lower bound on the…