Jack polynomials and some identities for partitions

We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack polynomials. These quantities are the moments of the "alpha-content" random variable with respect to some transition probability distributions.Comment: 22 pages, LaTeX, to appear in Trans. Amer. Math. So

Zero biasing and growth processes

The tools of zero biasing are adapted to yield a general result suitable for analyzing the behavior of certain growth processes. The main theorem is applied to prove central limit theorems, with explicit error terms in the L^1 metric, for certain statistics of the Jack measure on partitions and for the number of balls drawn in a Polya-Eggenberger urn process.Comment: 21 pages. Error in one term of the bound of the main theorem has been corrected, resulting in some changes to the bound for urn proces

Scaling Limit of the Spectral Distributions of the Laplacians on Large Graphs

This is the proceedings of the 2nd Japanese-German Symposium on Infinite Dimensional Harmonic Analysis held from September 20th to September 24th 1999 at the Department of Mathematics of Kyoto University.この論文集は, 1999年9月20日から9月24日の日程で京都大学理学研究科数学教室において開催された第2回日独セミナー「無限次元調和解祈」の成果をもとに編集されたものである.編集 : ハーバート・ハイヤー, 平井 武, 尾畑 信明Editors: Herbert Heyer, Takeshi Hirai, Nobuaki Obata #enWe examine several scaling limits of the spectral distributions of Laplacians (or equivalently adjacency operators) on regular graphs and their second quantization on Fock spaces as the graphs grow infinitely in certain manners