4,425 research outputs found
Two ways to solve ASEP
The purpose of this article is to describe the two approaches to compute
exact formulas (which are amenable to asymptotic analysis) for the probability
distribution of the current of particles past a given site in the asymmetric
simple exclusion process (ASEP) with step initial data. The first approach is
via a variant of the coordinate Bethe ansatz and was developed in work of Tracy
and Widom in 2008-2009, while the second approach is via a rigorous version of
the replica trick and was developed in work of Borodin, Sasamoto and the author
in 2012.Comment: 10 pages, Chapter in "Topics in percolative and disordered systems
Multiple regions of quantum criticality in YbAgGe
Dilation and thermopower measurements on YbAgGe, a heavy-fermion
antiferromagnet, clarify and refine the magnetic field-temperature (H-T) phase
diagram and reveal a field-induced phase with T-linear resistivity. On the
low-H side of this phase we find evidence for a first-order transition and
suggest that YbAgGe at 4.5 T may be close to a quantum critical end point. On
the high-H side our results are consistent with a second-order transition
suppressed to a quantum critical point near 7.2 T. We discuss these results in
light of global phase diagrams proposed for Kondo lattice systems
Patient-Based Outcomes After Tibia Fracture in Children and Adolescents
Introduction : Tibia fractures are common in pediatric patients and time necessary to return to normal function may be underappreciated. The purpose of this study was to assess functional recovery in pediatric patients who sustain tibia fractures, utilizing the Pediatrics Outcome Data Collection Instrument (PODCI), in order to provide evidence-based information on post-injury functional limitations and anticipated recovery times. Methods : 84patients (out of 264 eligible patients, response rate 32%) age 1.5-18 years treated for a tibia fracture at a large children's hospital between 1/07 and 4/08 completed a PODCI questionnaire at 6 and 12 months post-injury. PODCI questionnaires were compared to previously reportednormal controls using Student's t-test in six categories. Results : At 6 months after injury, the Sports functioning PODCI score was significantly less than healthy controls in both the parent reports for adolescent (mean 88.71 versus 95.4) and adolescent self-report (mean 90.44 versus 97.1); these showed no difference at 12 months. Discussion : For adolescents who sustain fractures of the tibia, there remains a negative impact on their sports functioning after 6 months that resolves by 12 months. Physicians can counsel their patients that although they may be limited in their sports function for some time after injury, it is anticipated that this will resolve by one year from the time of injury. Level of Evidence : Level II
{\bf -Function Evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles}
It has recently been emphasized that all known exact evaluations of gap
probabilities for classical unitary matrix ensembles are in fact
-functions for certain Painlev\'e systems. We show that all exact
evaluations of gap probabilities for classical orthogonal matrix ensembles,
either known or derivable from the existing literature, are likewise
-functions for certain Painlev\'e systems. In the case of symplectic
matrix ensembles all exact evaluations, either known or derivable from the
existing literature, are identified as the mean of two -functions, both
of which correspond to Hamiltonians satisfying the same differential equation,
differing only in the boundary condition. Furthermore the product of these two
-functions gives the gap probability in the corresponding unitary
symmetry case, while one of those -functions is the gap probability in
the corresponding orthogonal symmetry case.Comment: AMS-Late
Universal singularity at the closure of a gap in a random matrix theory
We consider a Hamiltonian , in which is a given
non-random Hermitian matrix,and is an Hermitian random matrix
with a Gaussian probability distribution.We had shown before that Dyson's
universality of the short-range correlations between energy levels holds at
generic points of the spectrum independently of . We consider here the
case in which the spectrum of is such that there is a gap in the
average density of eigenvalues of which is thus split into two pieces. When
the spectrum of is tuned so that the gap closes, a new class of
universality appears for the energy correlations in the vicinity of this
singular point.Comment: 20pages, Revtex, to be published in Phys. Rev.
Crossover to the KPZ equation
We characterize the crossover regime to the KPZ equation for a class of
one-dimensional weakly asymmetric exclusion processes. The crossover depends on
the strength asymmetry () and it occurs at
. We show that the density field is a solution of an
Ornstein-Uhlenbeck equation if , while for it is
an energy solution of the KPZ equation. The corresponding crossover for the
current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012),
813-82
Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile
We complement a recent exact study by L. Samaj on the properties of a guest
charge immersed in a two-dimensional electrolyte with charges . In
particular, we are interested in the behavior of the density profiles and
electric potential created by the charge and the electrolyte, and in the
determination of the renormalized charge which is obtained from the
long-distance asymptotics of the electric potential. In Samaj's previous work,
exact results for arbitrary coulombic coupling were obtained for a
system where all the charges are points, provided and .
Here, we first focus on the mean field situation which we believe describes
correctly the limit but large. In this limit we can
study the case when the guest charge is a hard disk and its charge is above the
collapse value . We compare our results for the renormalized charge
with the exact predictions and we test on a solid ground some conjectures of
the previous study. Our study shows that the exact formulas obtained by Samaj
for the renormalized charge are not valid for , contrary to a
hypothesis put forward by Samaj. We also determine the short-distance
asymptotics of the density profiles of the coions and counterions near the
guest charge, for arbitrary coulombic coupling. We show that the coion density
profile exhibit a change of behavior if the guest charge becomes large enough
(). This is interpreted as a first step of the counterion
condensation (for large coulombic coupling), the second step taking place at
the usual Manning--Oosawa threshold
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
A multi-layer extension of the stochastic heat equation
Motivated by recent developments on solvable directed polymer models, we
define a 'multi-layer' extension of the stochastic heat equation involving
non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio
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