Related papers: Expected Coalescence Time for a Nonuniform Allocat…
Let $X^I_n$ be the coalescence time of two particles picked at random from the $n$th generation of a critical Galton-Watson process with immigration, and let $A^I_n$ be the coalescence time of the whole population in the $n$th generation.…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds on the probabilities of both fast and…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
We consider a fully asymmetric one-dimensional model with mass-conserving coalescence. Particles of unit mass enter at one edge of the chain and coalescence while performing a biased random walk towards the other edge where they exit. The…
This paper provides a mathematical framework for estimation of the service time distribution and the expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process, in the case of partial…
We consider the exclusion process on segments of the integers in a site-dependent random environment. We assume to be in the ballistic regime in which a single particle has positive linear speed. Our goal is to study the mixing time of the…
We introduce a generalised relaxation-time-approximation form of the collision term in the Boltzmann kinetic equation that allows for using different relaxation times for elastic and inelastic collisions. The efficacy of the proposed…
Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the…
We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To…
The nodes are traditionally viewed as fixed points where the probability density vanishes. However, this work demonstrates that these nodes exhibit time-dependent oscillation in quantum superposition states. We derive this effect for a…
We revisit the discrete additive and multiplicative coalescents, starting with $n$ particles with unit mass. These cases are known to be related to some "combinatorial coalescent processes": a time reversal of a fragmentation of Cayley…
Quantum computing is gaining attention as a new approach for solving complex problems in many scientific fields. In atmospheric and oceanic sciences, it may help reduce computational costs of simulating large and nonlinear systems. However,…
We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
Consider a system of coalescing random walks where each individual performs random walk over a finite graph G, or (more generally) evolves according to some reversible Markov chain generator Q. Let C be the first time at which all walkers…
We study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions. For a scalar quantum field theory we show that generic time-reversal invariant evolutions approach…
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…
Conformal prediction can yield statistically valid prediction intervals for any regression model, with no model modifications and small computational costs. To assess its practical value, we apply conformal methods to quantify uncertainty…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…