论文信息 - Random permutations and Brownian motion

Random permutations and Brownian motion

On considere les cycles de permutation aleatoire de longueur n. Soit X n (t) le nombre des cycles de longueur n'exedant pas n t , T∈[0,1]. On montre que le processus aleatoire Y n (t)=(X n (t)-tl n n)/L n 1/2 n converge faiblement vers le mouvement brownien standard W(T), te[0,1]

Boris Pittel | B. Pittel | J. DeLaurentis | John Delaurentis

[1] L. A. Shepp,et al. Ordered cycle lengths in a random permutation , 1966 .

[2] P. Erdös,et al. On some problems of a statistical group-theory. I , 1965 .

[3] L. Lovász. Combinatorial problems and exercises , 1979 .

[4] V. E. Stepanov. Limit Distributions of Certain Characteristics of Random Mappings , 1969 .

[5] P. Erdos,et al. On some problems of a statistical group-theory. II , 1967 .

[6] J. D. T. Oliveira,et al. The Asymptotic Theory of Extreme Order Statistics , 1979 .

[7] M. R. Best. The distribution of some variables on symmetric groups , 1970 .

[8] Feller William,et al. An Introduction To Probability Theory And Its Applications , 1950 .

[9] WAITINGTIMES BETWEEN RECORD OBSERVATIONS , 1967 .

[10] G. Sankaranarayanan,et al. Ordered cycle lengths in a random permutation. , 1971 .

[11] C. L. Mallows,et al. Some Aspects of the Random Sequence , 1965 .

[12] David R. Cox,et al. The Theory of Stochastic Processes , 1967, The Mathematical Gazette.