508 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
Free-energy distribution of the directed polymer at high temperature
We study the directed polymer of length in a random potential with fixed
endpoints in dimension 1+1 in the continuum and on the square lattice, by
analytical and numerical methods. The universal regime of high temperature
is described, upon scaling 'time' and space (with for the discrete model) by a continuum model with
-function disorder correlation. Using the Bethe Ansatz solution for the
attractive boson problem, we obtain all positive integer moments of the
partition function. The lowest cumulants of the free energy are predicted at
small time and found in agreement with numerics. We then obtain the exact
expression at any time for the generating function of the free energy
distribution, in terms of a Fredholm determinant. At large time we find that it
crosses over to the Tracy Widom distribution (TW) which describes the fixed
infinite limit. The exact free energy distribution is obtained for any time
and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to
Tracy Widom established, 1 figure changed
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
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
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
Extremal statistics of curved growing interfaces in 1+1 dimensions
We study the joint probability distribution function (pdf) of the maximum M
of the height and its position X_M of a curved growing interface belonging to
the universality class described by the Kardar-Parisi-Zhang equation in 1+1
dimensions. We obtain exact results for the closely related problem of p
non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M)
where \tau_M is there the time at which the maximal height M is reached. Our
analytical results, in the limit p \to \infty, become exact for the interface
problem in the growth regime. We show that our results, for moderate values of
p \sim 10 describe accurately our numerical data of a prototype of these
systems, the polynuclear growth model in droplet geometry. We also discuss
applications of our results to the ground state configuration of the directed
polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics
Letters. New results added for non-intersecting excursion
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
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