Related papers: Universal Randomness
We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is log-normal, with the average energy growing exponentially.…
Although time-dependent random media with short range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in 1D lattice random…
The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article we shall be mainly…
We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts…
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…
In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common…
We study stationary solutions to the continuity equation for weakly compressible flows. These describe non-equilibrium steady states of weakly dissipative dynamical systems. Compressibility is a singular perturbation that changes the steady…
We study the anomalous transport in systems of random walks (RW's) on comb-like lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x-direction, showing a…
The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources, which was considered by Pr\"ahofer and Spohn. Depending on the strength of the sources, the limiting…
We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the n-th moment <Z^n> of the partition function is given by the ground state energy…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out…
We study the Tracy-Widom (TW) distribution $f_\beta(a)$ in the limit of large Dyson index $\beta \to +\infty$. This distribution describes the fluctuations of the rescaled largest eigenvalue $a_1$ of the Gaussian (alias Hermite) ensemble…
We consider TASEP in continuous time with non-random initial conditions and arbitrary fixed density of particles rho. We show GOE Tracy-Widom universality of the one-point fluctuations of the associated height function. The result phrased…
We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct…
A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The…
The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A…
Using well-known results from statistical physics, concerning the almost-sure behavior of the free energy of directed polymers in a random medium, we prove that random tree codes achieve the distortion-rate function almost surely under a…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…