Related papers: Dynamical Evolution in Noncommutative Discrete Pha…
A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely…
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced…
The kinetic equation is crucial for understanding the statistical properties of stochastic processes, yet current equations, such as the classical Fokker-Planck, are limited to local analysis. This paper derives a new kinetic equation for…
In this study we explore the cosmological behavior of a non-minimally coupled scalar field that is linked to torsion gravity. We demonstrate the Sorkin-Schutz formalism with general power law teleparallel torsion coupling. The autonomous…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the…
We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric…
We demonstrate that periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schr\"{o}dinger (DNLS) equation can strongly facilitate creation of traveling solitons in the lattice. We predict this possibility in an…
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an…
Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to…
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…
Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently…
We study the behavior of classical dimer coverings of the square lattice - a paradigmatic model for systems subject to constraints - evolving under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
We break the mold in flow-based generative modeling by proposing a new model based on the damped wave equation, also known as telegrapher's equation. Similar to the diffusion equation and Brownian motion, there is a Feynman-Kac type…
The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order.…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a Win-Stay-Lose-Shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…