Related papers: Extreme hitting probabilities for diffusion
How long does it take a random searcher to visit all sites of a given domain? This time, known as the cover time, is a key observable to quantify the efficiency of exhaustive searches, which require a complete exploration of an area and not…
The time instant -- the first-passage time (FPT) -- when a diffusive particle (e.g., a ligand such as oxygen or a signalling protein) for the first time reaches an immobile target located on the surface of a bounded three-dimensional domain…
Biological events are often initiated when a random "searcher" finds a "target," which is called a first passage time (FPT). In some biological systems involving multiple searchers, an important timescale is the time it takes the slowest…
We consider the problem of discriminating finite-dimensional quantum processes, also called quantum supermaps, that can consist of multiple time steps. Obtaining the ultimate performance for discriminating quantum processes is of…
We study the target searching on the DNA for proteins in the presence of non-constant drift and non-Gaussian $\alpha$-stable L\'evy fluctuations. The target searching is realized by the facilitated diffusion process. The existing works are…
We study analytically and numerically the mean fastest first-passage time (fFPT) to an immobile target for an ensemble of $N$ independent finite-speed random searchers driven by dichotomous noise and described by the telegrapher's equation.…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
We study the classic problem in which a Searcher must locate a hidden point, also called the Hider in a network, starting from a root point. The network may be either bounded or unbounded, thus generalizing well-known settings such as…
A random search is a stochastic process representing the random motion of a particle (denoted as the searcher) that is terminated when it reaches (detects) a target particle or area the first time. In intermittent search the random motion…
Real-time probability forecasts for binary outcomes are routine in sports, online experimentation, medicine, and finance. Retrospective narratives, however, often hinge on pathwise extremes: for example, a forecast that becomes "90%…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
Redundancy in biology may be explained by the need to optimize extreme searching processes, where one or few among many particles are requested to reach the target like in human fertilization. We show that non-Gaussian rare fluctuations in…
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms,…
We consider the superposition of symmetric simple exclusion dynamics speeded-up in time, with spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We show that the mixing time has an exponential lower bound in…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
When does a diffusing particle reach its target for the first time? This first-passage time (FPT) problem is central to the kinetics of molecular reactions in chemistry and molecular biology. Here we explain the behavior of smooth FPT…
In this review, we present the encounter-based approach to target search problems, in which the diffusive dynamics is described by the joint probability of the position of the particle and the number of its encounters with a given target…
Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…