403 research outputs found
Superdiffusivity of asymmetric exclusion process in dimensions one and two
We prove that the diffusion coefficient for the asymmetric exclusion process
diverges at least as fast as in dimension and
in . The method applies to nearest and non-nearest neighbor asymmetric
exclusion processes
Biochemistry of nitrification in soil. 1. Kinetics of, and the effects of poisons on, soil nitrification as studied by a soil perfusion technique
[First paragraph] Nitrification is the process whereby nitrogen, in the form of the ammonium cation or in organic combination, is converted into the nitrate anion. Nitrification in soil has long been established as a biological process (Schloessing & Muntz, 1877, 1879), but some evidence that, under tropical conditions, a non-biological nitrification in soil may occur has recently accumulated
Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to a many body quantum boson system with
attractive interactions. Performing the summation over the entire spectrum of
excited states the problem is reduced to the Fredholm determinant with the Airy
kernel which is known to yield the Tracy-Widom distributionComment: 5 page
Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the dynamical large deviations for a particle system in which
particles may have different velocities. We assume that we have two infinite
reservoirs of particles at the boundary: this is the so-called boundary driven
process. The dynamics we considered consists of a weakly asymmetric simple
exclusion process with collision among particles having different velocities
A Fredholm Determinant Representation in ASEP
In previous work the authors found integral formulas for probabilities in the
asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics
are uniquely determined once the initial state is specified. In this note we
restrict our attention to the case of step initial condition with particles at
the positive integers, and consider the distribution function for the m'th
particle from the left. In the previous work an infinite series of multiple
integrals was derived for this distribution. In this note we show that the
series can be summed to give a single integral whose integrand involves a
Fredholm determinant. We use this determinant representation to derive
(non-rigorously, at this writing) a scaling limit.Comment: 12 Pages. Version 3 includes a scaling conjectur
Occupation times of long-range exclusion and connections to KPZ class exponents
With respect to a class of long-range exclusion processes on \ZZ^d, with single particle transition rates of order , starting under Bernoulli invariant measure with density , we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on , and with respect to the variance of these functionals and associated scaling limits.
In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter .
However, in the asymmetric case, we study the asymptotics of the variances, which when and points to a curious dichotomy between long-range strength parameters . In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.The research of CB was supported in part by the French Ministry of Education through the grant ANR JCJC EDNHS. PG thanks FCT (Portugal) for support through the research project PTDC/MAT/109844/2009 and CNPq (Brazil) for support through the research project 480431/2013-2. PG thanks CMAT for support by "FEDER" through the "Programa Operacional Factores de Competitividade COMPETE" and by FCT through the project PEst-C/MAT/UI0013/2011. SS was supported in part by ARO grant W911NF-14-1-0179
Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
The distribution function of the free energy fluctuations in one-dimensional
directed polymers with -correlated random potential is studied by
mapping the replicated problem to the -particle quantum boson system with
attractive interactions. We find the full set of eigenfunctions and eigenvalues
of this many-body system and perform the summation over the entire spectrum of
excited states. It is shown that in the thermodynamic limit the problem is
reduced to the Fredholm determinant with the Airy kernel yielding the universal
Tracy-Widom distribution, which is known to describe the statistical properties
of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page
Airy processes and variational problems
We review the Airy processes; their formulation and how they are conjectured
to govern the large time, large distance spatial fluctuations of one
dimensional random growth models. We also describe formulas which express the
probabilities that they lie below a given curve as Fredholm determinants of
certain boundary value operators, and the several applications of these
formulas to variational problems involving Airy processes that arise in
physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI
Proceedings: Topics in percolative and disordered systems
Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient
We prove a law of large numbers and a central limit theorem for a tagged
particle in a symmetric simple exclusion process in the one-dimensional lattice
with variable diffusion coefficient. The scaling limits are obtained from a
similar result for the current through -1/2 for a zero-range process with bond
disorder. For the CLT, we prove convergence to a fractional Brownian motion of
Hurst exponent 1/4.Comment: 9 page
Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle
Stochastic lattice gases with degenerate rates, namely conservative particle
systems where the exchange rates vanish for some configurations, have been
introduced as simplified models for glassy dynamics. We introduce two
particular models and consider them in a finite volume of size in
contact with particle reservoirs at the boundary. We prove that, as for
non--degenerate rates, the inverse of the spectral gap and the logarithmic
Sobolev constant grow as . It is also shown how one can obtain, via a
scaling limit from the logarithmic Sobolev inequality, the exponential decay of
a macroscopic entropy associated to a degenerate parabolic differential
equation (porous media equation). We analyze finally the tagged particle
displacement for the stationary process in infinite volume. In dimension larger
than two we prove that, in the diffusive scaling limit, it converges to a
Brownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure
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