ﻻ يوجد ملخص باللغة العربية
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles with constant speed and transitions between discreet allowed velocity directions. A new ingredient is that transitions into a given velocity state depend on spatial derivatives of other states populations, rather than on populations themselves. This feature requires the sacrifice of the single-particle character of the model, but allows to imitate the Huygens principle and to recover wave equations in arbitrary dimensions.
Many dynamics are random processes with increments given by a quadratic form of a fast Gaussian process. We find that the rate function which describes path large deviations can be computed from the large interval asymptotic of a certain Fredholm det
In this paper, stochastic inertial manifold for damped wave equations subjected to additive white noise is constructed by the Lyapunov-Perron method. It is proved that when the intensity of noise tends to zero the stochastic inertial manifold converges to its deterministic counterpart almost surely.
We investigate an averaging process that describes how interacting agents approach consensus through binary interactions. In each elementary step, two agents are selected at random and they reach compromise by adopting their opinion average. We show
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations u u_{tt}+u_t=D u+f(u)+ u^alphadot{W} on a bounded spatial domain. An asymptoti
We investigate the behavior of the return amplitude ${cal F}(t)= |langlePsi(0)|Psi(t)rangle|$ following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension $d-1$ and linear size $O(L)$, from a state $|Psi(0)r