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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…
We study a system of branching Brownian motions on $\mathbb R$ with annihilation: at each branching time a new particle is created and the leftmost one is deleted. In [7] it has been studied the case of strictly local creations (the new…
We study the Fleming-Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…
We consider random normal matrix and planar symplectic ensembles, which can be interpreted as two-dimensional Coulomb gases having determinantal and Pfaffian structures, respectively. For general radially symmetric potentials, we derive the…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
The Fourier transformation is an effective and efficient operation of Gaussianization at the one-point level. Using a set of N-body simulation data, we verified that the one-point distribution functions of the dark matter momentum…
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…
We investigate three different methods to tackle the problem of diffusion-limited reactions (annihilation) of hard-core classical particles in one dimension. We first extend an approach devised by Lushnikov and calculate for a single…
The explicit computation of amplitudes for fermionic Gaussian pure states in arbitrary Pauli bases is a long-standing challenge in quantum many-body physics, with significant implications for quantum tomography, experimental studies, and…
We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the…
Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce…
We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the…
An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…
We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the…
It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
The phenomenon of Bose-like condensation, the continuous change of the dimensionality of the particle distribution as a consequence of freezing out of one or more degrees of freedom in the low particle density limit, is investigated…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
We prove that the tagged particles of infinitely many Brownian particles in $ \Rtwo $ interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature $ \beta = 2 $ are sub-diffusive. The associated delabeled…