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A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…
We show that the density of states of random wave equations, normalized by the square of the frequency, has a peak - sometimes narrow and sometimes broad - in the range of wave vectors between the disorder correlation length and the…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the statistical instability of the wave energy…
Different electron acceleration regimes in the evanescent field of a surface plasma wave are studied by considering the interaction of a test electron with the high-frequency electromagnetic field of a surface wave. The non-relativistic and…
An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for…
Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We…
We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow…
We study, globaly in time, the velocity distribution $f(v,t)$ of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field $E$. The density $f$ satisfies a…
We address a system of weakly interacting particles where the heterogenous connections among the particles are described by a graph sequence and the number of particles grows to infinity. Our results extend the existing law of large numbers…
We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…
The description of electron-electron interactions in transport problems is both analytically and numerically difficult. Here we show that a much simpler description of electron transport in the presence of interactions can be achieved in…
Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…
We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…
The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. One such material, graphene, is not only an excellent platform for the experimental realization of the…
Choice models for populations of agents on graphs are studied in terms of statistical thermodynamics. Equations of state are derived and discussed for different connectivity schemes, utility approximations, and temperature and volume…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…