Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 14 (2009) > Paper 81 open journal systems 


A functional combinatorial central limit theorem

Andrew D Barbour, Universitat Zurich
Svante Janson, Uppsala universitet


Abstract
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original random process. Distance is measured by comparison of expectations of smooth functionals of the processes, and the argument is by way of Stein's method. The pre-limiting process is then shown, under weak conditions, to converge to a Gaussian limit process. The theorem is used to describe the shape of random permutation tableaux.


Full text: PDF

Pages: 2352-2370

Published on: October 30, 2009
Bibliography
  1. R. J. Adler & J. E. Taylor (2007) Random Fields and Geometry. Springer, New York. MR2319516 (2008m:60090)
  2. A. D. Barbour (1990) Stein's method for diffusion approximation. Prob. Theory Rel. Fields 84, 297--322. MR1035659 (91d:60081)
  3. P. Billingsley (1968) Convergence of Probability Measures. Wiley, New York. MR0233396 (38 #1718)
  4. E. Bolthausen (1984) An estimate of the remainder in a combinatorial central limit theorem. Z. Wahrscheinlichkeit verw. Geb. 66, 379--386. MR0751577 (85j:60032)
  5. P. Hitczenko & S. Janson (2009) Asymptotic normality of statistics on permutation tableaux. Preprint, arXiv:0904.1222
  6. W. Hoeffding (1951) A combinatorial central limit theorem. Ann. Math. Stat. 22, 558--566. MR0044058 (13,363b)
  7. M. R. Leadbetter, G. Lindgren & H. Rootzén (1983) Extremes and Related Properties of Random Sequences and Processes. Springer, New York. MR0691492 (84h:60050)
  8. G. R. Shorack & J. A. Wellner (1986) Empirical Processes with Applications to Statistics. Wiley, New York. MR0838963 (88e:60002)
  9. E. Steingrímsson & L. K. Williams (2007) Permutation tableaux and permutation patterns. J. Comb. Theory, Ser. A 114, 211--234. MR2293088 (2008c:05004)















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489