排序方式: 共有41条查询结果,搜索用时 15 毫秒
1.
We study the rate of convergence of symmetric random walks on finite groups to the uniform distribution. A notion of moderate growth is introduced that combines with eigenvalue techniques to give sharp results. Roughly, for finite groups of moderate growth, a random walk supported on a set of generators such that the diameter of the group is requires order 2 steps to get close to the uniform distribution. This result holds for nilpotent groups with constants depending only on the number of generators and the class. Using Gromov's theorem we show that groups with polynomial growth have moderate growth. 相似文献
2.
We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have been studied in physics as simple exemplars of systems exhibiting slow relaxation. In our East model the natural conjecture is that the relaxation time (p), that is 1/(spectral gap), satisfies log (p)
as p0. We prove this up to a factor of 2. The upper bound uses the Poincaré comparison argument applied to a wave (long-range) comparison process, which we analyze by probabilistic techniques. Such comparison arguments go back to Holley (1984, 1985). The lower bound, which atypically is not easy, involves construction and analysis of a certain coalescing random jumps process. 相似文献
3.
Bump Daniel Diaconis Persi Keller Joseph B. 《Mathematical Physics, Analysis and Geometry》2002,5(2):101-123
Let M be a unitary matrix with eigenvalues t
j
, and let f be a function on the unit circle. Define X
f
(M)=f(t
j
). We derive exact and asymptotic formulae for the covariance of X
f
and X
g
with respect to the measures |(M)|2dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest. 相似文献
4.
This paper gives an abstract version of de Finettis theorem that characterizes mixing measures with Lp densities. The general setting is reviewed; after the theorem is proved, it is specialized to coin tossing and to exponential random variables. Laplace transforms of bounded densities are characterized, and inversion formulas are discussed. 相似文献
5.
Repeated convolution of a probability measure on leads to the central limit theorem and other limit theorems. This paper investigates what kinds of results remain without positivity. It reviews theorems due to Schoenberg, Greville, and Thomée which are motivated by applications to data smoothing (Schoenberg and Greville) and finite difference schemes (Thomée). Using Fourier transform arguments, we prove detailed decay bounds for convolution powers of finitely supported complex functions on . If M is an hermitian contraction, an estimate for the off‐diagonal entries of the powers of is obtained. This generalizes the Carne–Varopoulos Markov chain estimate. 相似文献
6.
We derive closed form expressions and limiting formulae for a variety of functions of a permutation resulting from repeated
riffle shuffles. The results allow new formulae and approximations for the number of permutations inS
n with given cycle type and number of descents. The theorems are derived from a bijection discovered by Gessel. A self-contained
proof of Gessel's result is given. 相似文献
7.
Persi Diaconis Steven N. Evans 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):863
We study a class of Gaussian random fields with negative correlations. These fields are easy to simulate. They are defined in a natural way from a Markov chain that has the index space of the Gaussian field as its state space. In parallel with Dynkin's investigation of Gaussian fields having covariance given by the Green's function of a Markov process, we develop connections between the occupation times of the Markov chain and the prediction properties of the Gaussian field. Our interest in such fields was initiated by their appearance in random matrix theory. 相似文献
8.
J. J. Whitmore F. Persi W. S. Toothacker P. A. Elcombe J. C. Hill W. W. Neale W. D. Walker W. Kowald P. Lucas L. Voyvodic R. Ammar D. Coppage R. Davis J. Gress S. Kanekal N. Kwak J. M. Bishop N. N. Biswas N. M. Cason V. P. Kenney M. C. K. Mattingly R. C. Ruchti W. D. Shephard 《Zeitschrift fur Physik C Particles and Fields》1994,62(2):199-227
9.
Persi?Diaconis Gilles?LebeauEmail author Laurent?Michel 《Inventiones Mathematicae》2011,185(2):239-281
This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevant Markov operators, that
give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original application of the Metropolis algorithm. 相似文献
10.