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101.
On the distribution of the length of the longest increasing subsequence of random permutations 总被引:18,自引:0,他引:18
Jinho Baik Percy Deift Kurt Johansson 《Journal of the American Mathematical Society》1999,12(4):1119-1178
The authors consider the length, , of the longest increasing subsequence of a random permutation of numbers. The main result in this paper is a proof that the distribution function for , suitably centered and scaled, converges to the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is based on the steepest descent method for Riemann-Hilbert problems, introduced by Deift and Zhou in 1993 in the context of integrable systems. The applicability of the Riemann-Hilbert technique depends, in turn, on the determinantal formula of Gessel for the Poissonization of the distribution function of .
102.
The Ising model with competing interactions is studied in a mean field effective medium approach. The phase diagram of such
model alloys is studied. We conclude that for all ratios of the competing interaction moments, a spin glass phase always exists
at low temperatures for certain concentration regimes. 相似文献
103.
Random walks on lattices. IV. Continuous-time walks and influence of absorbing boundaries 总被引:1,自引:0,他引:1
The general study of random walks on a lattice is developed further with emphasis on continuous-time walks with an asymmetric bias. Continuous time walks are characterized by random pauses between jumps, with a common pausing time distribution(t). An analytic solution in the form of an inverse Laplace transform for P(l, t), the probability of a walker being atl at timet if it started atl
o att=0, is obtained in the presence of completely absorbing boundaries. Numerical results for P(l, t) are presented for characteristically different (t), including one which leads to a non-Gaussian behavior for P(l, t) even for larget. Asymptotic results are obtained for the number of surviving walkers and the mean l showing the effect of the absorption at the boundary.This study was partially supported by ARPA and monitored by ONR(N00014-17-0308). 相似文献
104.
Oseen’ approximations are used to study the slow motion of a viscous, incompressible, electrically conducting fluid past a
circular cylinder in the presence of a uniform aligned magnetic field. Using series truncation method, the analytical solutions
for the first three terms in the Fourier sine series expansion of the stream function are obtained. Numerical values of the
tangential drag for different values of magnetic interaction parameter and viscous Reynolds number are calculated. 相似文献
105.
Michael Nauenberg 《Journal of statistical physics》1985,41(5-6):803-810
Applying scaling and universality arguments, the long-time behavior of the probability distribution for a random walk in a one-dimensional random medium satisfying Sinai's constraint is obtained analytically. The convergence to this asymptotic limit and the fluctuations of this distribution are evaluated by solving numerically the stochastic equations for this walk. 相似文献
106.
Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total
reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first
derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by
channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and
reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It
becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width
and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial
for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling
only occurs in a finite range of ɛ. 相似文献
107.
Random coil phosphorus chemical shift of deoxyribonucleic acids 总被引:1,自引:0,他引:1
Random coil phosphorus chemical shift has been studied using 16 17-nucleotide DNA sequences. Due to the presence of residual base stacking in these sequences, the temperature and sequence effects were investigated at 50 and 55 degrees C. The phosphorus chemical shifts of random coil DNA sequences have been found to be independent of temperature. Sequence effect analysis shows that the phosphorus chemical shift of a nucleotide in a random coil DNA sequence depends on both its 5'- and 3'-nearest neighbors. A trimer model has been used to establish the random coil 31P chemical shift prediction protocol which shows an accuracy of 0.02 ppm. 相似文献
108.
Peter?EichelsbacherEmail author Matthias?L?we 《Probability Theory and Related Fields》2004,130(4):441-472
We derive moderate deviation principles for the overlap parameter in the Hopfield model of spin glasses and neural networks. If the inverse temperature is different from the critical inverse temperature c=1 and the number of patterns M(N) satisfies M(N)/N 0, the overlap parameter multiplied by N, 1/2 < < 1, obeys a moderate deviation principle with speed N1–2 and a quadratic rate function (i.e. the Gaussian limit for = 1/2 remains visible on the moderate deviation scale). At the critical temperature we need to multiply the overlap parameter by N, 1/4 < < 1. If then M(N) satisfies (M(N)6 log N M(N)2N4 log N)/N 0, the rescaled overlap parameter obeys a moderate deviation principle with speed N1–4 and a rate function that is basically a fourth power. The random term occurring in the Central Limit theorem for the overlap at c = 1 is no longer present on a moderate deviation scale. If the scaling is even closer to N1/4, e.g. if we multiply the overlap parameter by N1/4 log log N the moderate deviation principle breaks down. The case of variable temperature converging to one is also considered. If N converges to c fast enough, i.e. faster than the non-Gaussian rate function persists, whereas for N converging to one slower than the moderate deviations principle is given by the Gaussian rate. At the borderline the moderate deviation rate function is the one at criticality plus an additional Gaussian term.Research supported by the Volkswagen-Stiftung (RiP-program at Oberwolfach, Germany).Mathematics Subject Classification (2000): 60F10 (primary), 60K35, 82B44, 82D30 (secondary) 相似文献
109.
Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and a constraint is chosen from also uniformly at random. This procedure is repeated m times independently. We are interested in whether the resulting linear programming problem is feasible. We prove that the feasibility property experiences a linear phase transition, when n and m = cn for a constant c. Namely, there exists a critical value c* such that, when c < c*, the problem is feasible or is asymptotically almost feasible, as n, but, when c>c*, the distance to feasibility is at least a positive constant independent of n. Our result is obtained using the combination of a powerful local weak convergence method developed in Aldous [Ald92], [Ald01], Aldous and Steele [AS03], Steele [Ste02] and martingale techniques. By exploiting a linear programming duality, our theorem implies the following result in the context of sparse random graphs G(n, cn) on n nodes with cn edges, where edges are equipped with randomly generated weights. Let (n, c) denote maximum weight matching in G(n, cn). We prove that when c is a constant and n , the limit limn (n, c)/n, exists, with high probability. We further extend this result to maximum weight b-matchings also in G(n, cn). 相似文献
110.
In this paper we consider random perturbations of dynamical systems and diffusion processes with a first integral. We calculate, under some assumptions, the limiting behavior of the slow component of the perturbed system in an appropriate time scale for a general class of perturbations. The phase space of the slow motion is a graph defined by the first integral. This is a natural generalization of the results concerning random perturbations of Hamiltonian systems. Considering diffusion processes as the unperturbed system allows to study the multidimensional case and leads to a new effect: the limiting slow motion can spend non-zero time at some points of the graph. In particular, such delay at the vertices leads to more general gluing conditions. Our approach allows one to obtain new results on singular perturbations of PDEs.
Mathematics Subject Classification (2001): 60H10; 34C29; 35B20 相似文献