Related papers: Exact calculation of the large deviation function …
As a strategy to complete games quickly, we investigate one-dimensional random walks where the step length increases deterministically upon each return to the origin. When the step length after the kth return equals k, the displacement of…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space,…
We present a coalescent process where three particles merge at each coagulation step. Using a random walk representation, we prove duality with a fragmentation process, whose fragmentation law we specify explicitly. Furthermore, we give a…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
We extend classical results by A. V. Nagaev [Izv. Akad. Nauk UzSSR Ser. Fiz.--Mat. Nauk 6 (1969) 17--22, Theory Probab. Appl. 14 (1969) 51--64, 193--208] on large deviations for sums of i.i.d. regularly varying random variables to partial…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme…
We study some aspects of the absorption time of the Beta$(a,b)$-Coalescent starting with $n$ blocks. More precisely, when $a>1$, the absorption time is known to converge to infinity as $n$ goes to infinity, and we prove that it satisfies a…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
The redundancy principle provides the framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. But what is $n$ large? To estimate large $n$ with respect…
In this paper, we investigate the precise local large deviation probabilities for random sums of independent real-valued random variables with a common distribution $F$, where $F(x+\Delta)=F((x, x+T])$ is an $\mathcal{O}$-regularly varying…
We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle…
We present approximation methods which lead to law of large numbers and fluctuation results for functionals of $\Lambda$-coalescents, both in the dust-free case and in the case with a dust component. Our focus is on the tree length (or…
We consider particle systems (also known as point processes) on the line and in the plane, and are particularly interested in "hole" events, when there are no particles in a large disk (or some other domain). We survey the extensive work on…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
When particles on a line collide, they may coalesce into one. Such systems arise in the voter model, where boundaries between opinion clusters perform coalescing random walks, and in reaction-diffusion theory, where diffusing particles…