We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in space-time regions where the medium is typical, we obtain a law of large numbers and an averaged central limit theorem for the walk via a regeneration constr...

We consider the homogenization of the wave equation with high frequency initial conditions propagating in a medium with highly oscillatory random coefficients. By appropriate mixing assumptions on the random medium, we obtain an error estimate between the exact wave solution and the homogenized wave solution in the energy norm. This allows us to consider the limiting behavior of the energy dens...

We have studied the aging effect on the dynamics of unbinding of a double stranded directed polymer in a random medium. By using the Monte Carlo dynamics of a lattice model in two dimensions, for which disorder is known to be relevant, the unbinding dynamics is studied by allowing the bound polymer to relax in the random medium for a waiting time and then allowing the two strands to unbind. The...

In this paper, we introduce a novel random scheduling strategy for distributed medium access in spreadspectrum (SS) and multipacket reception networks. The proposed random scheduling (RASC) protocol uses a special method of seed exchange in which the seeds are used for pseudo-random generation. The RASC utilizes the seeds for randomly decomposing the network into independent clusters containing...

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial diff...

We studied resonant laser interaction with Rb atoms confined to the interstitial cavities of a random porous glass. Due to diffusive light propagation, the effect of atomic absorption on the light scattered by the sample is almost entirely compensated by atomic fluorescence at low atomic densities. For higher densities, radiation trapping increases the probability of nonradiative decay via atom...

We consider the problem of the random fluctuations in the solutions to elliptic PDEs with highly oscillatory random coefficients. In our setting, as the correlation length of the fluctuations tends to zero, the heterogeneous solution converges to a deterministic solution obtained by averaging. When the Green’s function to the unperturbed operator is sufficiently singular (i.e., not square integ...

We report the studies of emission from a novel random amplifying medium that we term a “Lévy Laser” due to the non-Gaussian statistical nature of its emission over the ensemble of random realizations. It is observed that the amplification is dominated by certain improbable events that are “larger than rare”, which give the intensity statistics a Lévy like “fat tail”. This, to the best of our kn...

013602-1 We derive the photon number probability distribution of light emitted from a random multiple-lightscattering medium with gain, using a generalized master equation. Our model treats the random laser medium as a collection of low quality-factor cavities, coupled by random photon diffusion. We demonstrate that, with stronger scattering, the pumping threshold for the transition from chaoti...