共查询到20条相似文献,搜索用时 15 毫秒
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Kurt Johansson 《Communications in Mathematical Physics》2000,209(2):437-476
We study a certain random growth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE). 相似文献
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Victor Dotsenko 《Journal of statistical physics》2006,122(2):197-216
The explicit form of the Griffiths singularity in the random ferromagnetic Ising model in external magnetic field is derived.
In terms of the continuous random temperature Ginzburg-Landau Hamiltonian it is shown that in the paramagnetic phase away
from the critical point the free energy as the function of the external magnetic field h in the limit h → 0 has the essential singularity of the form exp [−(const)/hD/3] (where 1 < D < 4 is the space dimensionality). It is demonstrated that in terms of the replica formalism this contribution to the free
energy comes due to non-perturbative replica instanton excitations. 相似文献
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We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar Gibbs measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes. 相似文献
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Timo Seppäläinen 《Communications in Mathematical Physics》2002,229(1):141-182
We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with
are the Aldous–Diaconis–Hammersley process and the related stick model. The A-D-H process represents a particle configuration
on the line, or a 1-dimensional interface on the plane which moves in one fixed direction through random local jumps. The
stick model is the process of local slopes of the A-D-H process, and has a conserved quantity. The results describe the fluctuations
of these systems around the deterministic evolution to which the random system converges under hydrodynamic scaling. We look
at diffusive fluctuations, by which we mean fluctuations on the scale of the classical central limit theorem. In the scaling
limit these fluctuations obey deterministic equations with random initial conditions given by the initial fluctuations. Of
particular interest is the effect
of macroscopic shocks, which play a dominant role because dynamical noise is suppressed on the scale we are working.
Received: 4 October 2001 / Accepted: 12 March 2002 相似文献
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Alain-Sol Sznitman 《Communications in Mathematical Physics》1997,189(2):337-363
We investigate the principal Dirichlet eigenvalue of the Laplacian with soft Poissonian obstacles in large boxes of , d≥ 2. With the help of our recent version of the method of enlargement of obstacles [18], we derive quantitative confidence
intervals for these eigenvalues. We also provide less quantitative estimates, which however point out the correct size of
fluctuations, and indicate a stiffness in their behavior. In the two-dimensional case we derive geometric controls, which
relate these eigenvalues to certain empty circular droplets. Our results also have natural applications to the study of the
location of minima of certain intermittent random variational problems, motivated by [13, 17].
Received: 13 June 1996 / Accepted: 10 March 1997 相似文献
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A comparison between the standard adiabatic piston dynamics and that of a perfectly conducting (diathermal) piston helps to
clarify their different behaviors and, in particular, the anomalously large random displacement of the adiabatic piston as
compared to the diathermal one. It is shown to be associated with a situation where the presence of a single massive “particle”
(the piston), acting as an internal constraint in a many-particle system, plays a somewhat unexpected relevant role. A significant
physical insight accounting for the above difference is gained by means of a simple analysis of the phase space available
to our system. 相似文献
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Taro Nagao 《Journal of statistical physics》2007,129(5-6):1137-1158
It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of Pfaffians. In this article, we review the formulations and applications of Pfaffian formulas. For that purpose, we first present the general Pfaffian expressions in terms of the corresponding skew orthogonal polynomials. Then we clarify the relation to Eynard and Mehta’s determinant formula for hermitian matrix models and explain how the evaluation is simplified in the cases related to the classical orthogonal polynomials. Applications of Pfaffian formulas to random matrix theory and other fields are also mentioned. 相似文献
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Sean O’Rourke 《Journal of statistical physics》2010,138(6):1045-1066
We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an n×n matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let x k denote eigenvalue number k. Under the condition that both k and n?k tend to infinity as n→∞, we show that x k is normally distributed in the limit. We also consider the joint limit distribution of eigenvalues $(x_{k_{1}},\ldots,x_{k_{m}})$ from the GOE or GSE where k 1, n?k m and k i+1?k i , 1≤i≤m?1, tend to infinity with n. The result in each case is an m-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments. 相似文献
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J.B. Conrey D.W. Farmer J.P. Keating M.O. Rubinstein N.C. Snaith 《Communications in Mathematical Physics》2003,237(3):365-395
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly
with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric
polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously
obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather
than large-matrix asymptotic approximations. They also mirror exactly the autocorrelation formulae conjectured to hold for
L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory
and the theory of L-functions.
Received: 1 August 2002 / Accepted: 25 December 2002
Published online: 7 May 2003
Communicated by P. Sarnak 相似文献
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On the Uniqueness for the Spatially Homogeneous Boltzmann Equation with a Strong Angular Singularity
We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous
Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local
(in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedness result is shown for
all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying
to a strong angular singularity, except in the special case of Maxwell molecules.
Our proof relies on the ideas of Tanaka (Z. Wahrscheinlichkeitstheor. Verwandte. Geb. 46(1):67–105, [1978]) we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to
couple two such processes started with two different initial conditions, in such a way that they almost surely remain close
to each other. 相似文献
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Igor Wigman 《Communications in Mathematical Physics》2010,298(3):787-831
Using the multiplicities of the Laplace eigenspace on the sphere (the space of spherical harmonics) we endow the space with
Gaussian probability measure. This induces a notion of random Gaussian spherical harmonics of degree n having Laplace eigenvalue E = n(n + 1). We study the length distribution of the nodal lines of random spherical harmonics. 相似文献
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Universal limits for the eigenvalue correlation functions in the bulk of the spectrum are shown for a class of nondeterminantal
random matrices known as the fixed trace or the Hilbert-Schmidt ensemble. These universal limits have been proved before for
determinantal Hermitian matrix ensembles and for some special classes of the Wigner random matrices.
Research supported by Sonderforschungsbereich 701 “Spektrale Strukturen und Topologische Methoden in der Mathematik”.
Research supported by Sonderforschungsbereich 701 “Spektrale Strukturen und Topologische Methoden in der Mathematik,” and
grants RFBR-05-01-00911, DFG-RFBR-04-01-04000, and NS-638.2008.1. 相似文献
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本文概述了量子不可积性的拓扑观.按拓扑观点探讨了量子体系完全可积的条件,通向不可积的机制,以及在量子不可积条件下的能谱性质,从动力学角度阐明了随机矩阵理论的基础,还简要讨论了这些理论在核结构问题中的应用. Quantum nonintegrability is studied in a topological view.The condition for complete integrability of quantum systems and the mechanism leading to global nonintegrability are investigated.The basis of random matrix theory for describing energy spectra of nonintegrable quantum systems is clarified.Applications to nuclear structure are briefly discussed. 相似文献
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