Related papers: Nonlinear recombinations and generalized random tr…
We have formulated a kinetic theory for a condensed atomic gas in a trap, i.e., a generalized Gross-Pitaevskii equation, as well as a quantum-Boltzmann equation for the normal and anomalous fluctuations [R. Walser et al., Phys. Rev. A, 59,…
We study the discrete-time evolution of a transformation on a set of probability measures that is up-dated combining independently the marginals on the atoms of partitions. This model was recently introduced in Baake, Baake and Salamat…
We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop…
We study nonlinear dynamics of superposition of quantum wavepackets in various systems such as Kerr medium, Morse oscillator and bosonic Josephson junction. The prime reason behind this study is to find out how the superposition of states…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
We examine a non-reciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross diffusivities, provides a generic mechanism for the…
The evolution of a composite closed system using the integral wave equation with the kernel in the form of path integral is considered. It is supposed that a quantum particle is a subsystem of this system. The evolution of the reduced…
The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…
Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…
We consider a continuum aggregation model with nonlinear local repulsion given by a degenerate power-law diffusion with general exponent. The steady states and their properties in one dimension are studied both analytically and numerically,…
Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of…
We develop and present a generalization of the GN-model - the generalized Gaussian noise (GGN) model - to enabling a fair application of GN-model to predict generation of nonlinear interference when loss parameters relevantly vary with…
We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of $N$ particles, with the aim of quantifying how fast these degrees of freedom become chaotic in a time scale in…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
We review and classify stochastic processes without detailed balance condition. We obtain stationary distributions and investigate their stability in terms of generalized entropic divergences beyond the Kullback-Leibler formula. A simple…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…