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Coagulation and fragmentation (CF) is a fundamental process by which particles attach to each other to form clusters while existing clusters break up into smaller ones. It is a ubiquitous process that plays a key role in many physical and…
We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight on the…
The theory of diffusion seeks to describe the motion of particles in a chaotic environment. Classical theory models individual particles as independent random walkers, effectively forgetting that particles evolve together in the same…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different…
We consider an open quantum many-particle system in which there are dissipative processes. The evolution of this system is described by a kinetic equation for the density matrix. From the equation describing a random Markov process in this…
We consider a system of particles performing a discrete-time binary branching random walk with independent standard normal increments subject to a penalty $\b$ for every pair of particles that get within distance $\e$ of each other at every…
Suppose $k$ centers are fit to $m$ points by heuristically minimizing the $k$-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with $p\geq 4$ bounded moments; in…
We study processes with unstable particles in intermediate time-like states. It is shown that the amplitudes squared of such processes factor exactly in the framework of the model of unstable particles with continuous masses. Decay widths…
The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially…
We study the ensemble of complex symmetric matrices. The ensemble is useful in the study of effect of dissipation on systems with time reversal invariance. We consider the nearest neighbor spacing distribution and spacing ratio to…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles…
The eigenfunctions and eigenvalues of the master-equation for zero range process on a ring are found exactly via the Bethe ansatz. The rates of particle exit from a site providing the Bethe ansatz applicability are shown to be expressed in…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
Using the Bethe ansatz we obtain the exact solution for the one-dimensional asymmetric avalanche process. We evaluate the velocity of dispersive flow as a function of driving force and the density of particles. The obtained solution shows a…
A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…