Related papers: Local Central Limit Theorem for Reflecting Diffusi…
We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena…
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…
Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.
The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
We consider a Bose gas trapped in the unit torus in the Gross-Pitaevskii regime. In the ground state, we prove that fluctuations of bounded one-particle observables satisfy a central limit theorem.
We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolving family of curves driven by curve…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
The scattering of fast charged particles in a bent crystal has been analyzed in the framework of relativistic classical mechanics. The expressions obtained for the deflection function are in satisfactory agreement with the experimental data…
We prove a central limit theorem for the winding number of a directed polymer on a cylinder, which is equivalent with proving the Gaussian fluctuations of the endpoint of the directed polymer in a spatial periodic environment.
We study a class of high-frequency path functionals for diffusions with singular thresholds or boundaries, where the process exhibits either (i) skweness, oscillating coefficients, and stickiness, or (ii) sticky reflection. The functionals…
A nonlinear electromagnetic scattering problem is studied in the presence of bound states in the radiation continuum. It is shown that the solution is not analytic in the nonlinear susceptibility and the conventional perturbation theory…
The statistical scattering properties of wave transport in disordered waveguides are derived perturbatively within the transition matrix formalism. The limiting macroscopic statistic of the wave transport, emerges as a consequence of a…
Diffraction of elastic waves is considered for a system consisting of two parallel arrays of thin (subwavelength) cylinders that are arranged periodically. The embedding media supports waves with all polarizations, one longitudinal and two…
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…
At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to 1/A, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods),…
We consider a generalization of the so-called divide and color model recently introduced by Haggstrom. We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit…