8,917 research outputs found
Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation
We consider the polynomials orthonormal with respect to the weight on the unit circle in the complex plane. The leading coefficient
is found to satisfy a difference-differential (spatially discrete)
equation which is further proved to approach a third order differential
equation by double scaling. The third order differential equation is equivalent
to the Painlev\'e II equation. The leading coefficient and second leading
coefficient of can be expressed asymptotically in terms of the
Painlev\'e II function.Comment: 16 page
Universality in the profile of the semiclassical limit solutions to the focusing Nonlinear Schroedinger equation at the first breaking curve
We consider the semiclassical (zero-dispersion) limit of the one-dimensional
focusing Nonlinear Schroedinger equation (NLS) with decaying potentials. If a
potential is a simple rapidly oscillating wave (the period has the order of the
semiclassical parameter epsilon) with modulated amplitude and phase, the
space-time plane subdivides into regions of qualitatively different behavior,
with the boundary between them consisting typically of collection of piecewise
smooth arcs (breaking curve(s)). In the first region the evolution of the
potential is ruled by modulation equations (Whitham equations), but for every
value of the space variable x there is a moment of transition (breaking), where
the solution develops fast, quasi-periodic behavior, i.e., the amplitude
becomes also fastly oscillating at scales of order epsilon. The very first
point of such transition is called the point of gradient catastrophe. We study
the detailed asymptotic behavior of the left and right edges of the interface
between these two regions at any time after the gradient catastrophe. The main
finding is that the first oscillations in the amplitude are of nonzero
asymptotic size even as epsilon tends to zero, and they display two separate
natural scales; of order epsilon in the parallel direction to the breaking
curve in the (x,t)-plane, and of order epsilon ln(epsilon) in a transversal
direction. The study is based upon the inverse-scattering method and the
nonlinear steepest descent method.Comment: 40 pages, 10 figure
On ASEP with Step Bernoulli Initial Condition
This paper extends results of earlier work on ASEP to the case of step
Bernoulli initial condition. The main results are a representation in terms of
a Fredholm determinant for the probability distribution of a fixed particle,
and asymptotic results which in particular establish KPZ universality for this
probability in one regime. (And, as a corollary, for the current fluctuations.)Comment: 16 pages. Revised version adds references and expands the
introductio
Sample-to-sample fluctuations and bond chaos in the -component spin glass
We calculate the finite size scaling of the sample-to-sample fluctuations of
the free energy of the component vector spin glass in the
large- limit. This is accomplished using a variant of the interpolating
Hamiltonian technique which is used to establish a connection between the free
energy fluctuations and bond chaos. The calculation of bond chaos then shows
that the scaling of the free energy fluctuaions with system size is with , and very likely
exactly.Comment: 12 pages, 1 figur
From Random Matrices to Stochastic Operators
We propose that classical random matrix models are properly viewed as finite
difference schemes for stochastic differential operators. Three particular
stochastic operators commonly arise, each associated with a familiar class of
local eigenvalue behavior. The stochastic Airy operator displays soft edge
behavior, associated with the Airy kernel. The stochastic Bessel operator
displays hard edge behavior, associated with the Bessel kernel. The article
concludes with suggestions for a stochastic sine operator, which would display
bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics.
Changes in this revision: recomputed Monte Carlo simulations, added reference
[19], fit into margins, performed minor editin
On Orthogonal and Symplectic Matrix Ensembles
The focus of this paper is on the probability, , that a set
consisting of a finite union of intervals contains no eigenvalues for the
finite Gaussian Orthogonal () and Gaussian Symplectic ()
Ensembles and their respective scaling limits both in the bulk and at the edge
of the spectrum. We show how these probabilities can be expressed in terms of
quantities arising in the corresponding unitary () ensembles. Our most
explicit new results concern the distribution of the largest eigenvalue in each
of these ensembles. In the edge scaling limit we show that these largest
eigenvalue distributions are given in terms of a particular Painlev\'e II
function.Comment: 34 pages. LaTeX file with one figure. To appear in Commun. Math.
Physic
Asymptotics of a discrete-time particle system near a reflecting boundary
We examine a discrete-time Markovian particle system on the quarter-plane
introduced by M. Defosseux. The vertical boundary acts as a reflecting wall.
The particle system lies in the Anisotropic Kardar-Parisi-Zhang with a wall
universality class. After projecting to a single horizontal level, we take the
longtime asymptotics and obtain the discrete Jacobi and symmetric Pearcey
kernels. This is achieved by showing that the particle system is identical to a
Markov chain arising from representations of the infinite-dimensional
orthogonal group. The fixed-time marginals of this Markov chain are known to be
determinantal point processes, allowing us to take the limit of the correlation
kernel.
We also give a simple example which shows that in the multi-level case, the
particle system and the Markov chain evolve differently.Comment: 16 pages, Version 2 improves the expositio
Immune- and nonimmune-compartment-specific interferon responses are critical determinants of herpes simplex virus-induced generalized infections and acute liver failure
The interferon (IFN) response to viral pathogens is critical for host survival. In humans and mouse models, defects in IFN responses can result in lethal herpes simplex virus 1 (HSV-1) infections, usually from encephalitis. Although rare, HSV-1 can also cause fulminant hepatic failure, which is often fatal. Although herpes simplex encephalitis has been extensively studied, HSV-1 generalized infections and subsequent acute liver failure are less well understood. We previously demonstrated that IFN-αβγR-/- mice are exquisitely susceptible to liver infection following corneal infection with HSV-1. In this study, we used bone marrow chimeras of IFN-αβγR-/- (AG129) and wild-type (WT; 129SvEv) mice to probe the underlying IFN-dependent mechanisms that control HSV-1 pathogenesis. After infection, WT mice with either IFN-αβγR-/- or WT marrow exhibited comparable survival, while IFN-αβγR-/- mice with WT marrow had a significant survival advantage over their counterparts with IFN-αβγR-/- marrow. Furthermore, using bioluminescent imaging to maximize data acquisition, we showed that the transfer of IFN-competent hematopoietic cells controlled HSV-1 replication and damage in the livers of IFN-αβγR-/- mice. Consistent with this, the inability of IFN-αβγR-/- immune cells to control liver infection in IFN-αβγR-/- mice manifested as profoundly elevated aspartate transaminase (AST) and alanine transaminase (ALT) levels, indicative of severe liver damage. In contrast, IFN-αβγR-/-mice receiving WT marrow exhibited only modest elevations of AST and ALT levels. These studies indicate that IFN responsiveness of the immune system is a major determinant of viral tropism and damage during visceral HSV infections
Formulas for ASEP with Two-Sided Bernoulli Initial Condition
For the asymmetric simple exclusion process on the integer lattice with
two-sided Bernoulli initial condition, we derive exact formulas for the
following quantities: (1) the probability that site x is occupied at time t;
(2) a correlation function, the probability that site 0 is occupied at time 0
and site x is occupied at time t; (3) the distribution function for the total
flux across 0 at time t and its exponential generating function.Comment: 18 page
Generalization of the Poisson kernel to the superconducting random-matrix ensembles
We calculate the distribution of the scattering matrix at the Fermi level for
chaotic normal-superconducting systems for the case of arbitrary coupling of
the scattering region to the scattering channels. The derivation is based on
the assumption of uniformly distributed scattering matrices at ideal coupling,
which holds in the absence of a gap in the quasiparticle excitation spectrum.
The resulting distribution generalizes the Poisson kernel to the nonstandard
symmetry classes introduced by Altland and Zirnbauer. We show that unlike the
Poisson kernel, our result cannot be obtained by combining the maximum entropy
principle with the analyticity-ergodicity constraint. As a simple application,
we calculate the distribution of the conductance for a single-channel chaotic
Andreev quantum dot in a magnetic field.Comment: 7 pages, 2 figure
- …