A CLT Plancherel representations of the infinite-dimensional unitary group

被引:0
作者
Borodin A. [1 ,2 ,3 ]
Bufetov A. [2 ,3 ,4 ]
机构
[1] Massachusetts Institute of Technology, Cambridge
[2] Institute for Information Transmission Problems, Moscow
[3] Institute for Information Transmission Problems, Moscow
[4] Independent University of Moscow, Moscow
关键词
Gaussian Process; Random Matrice; Unitary Group; Free Field; Gaussian Free Field;
D O I
10.1007/s10958-013-1257-1
中图分类号
学科分类号
摘要
We study the asymptotics of traces of (noncommutative) monomials formed by the images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process that can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian free fields. The limiting process has previously arisen via the global scaling limit of submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere. Bibliography: 14 titles. © 2013 Springer Science+Business Media New York.
引用
收藏
页码:419 / 426
页数:7
相关论文
共 14 条
  • [1] Biane P., Approximate factorization and concentration for characters of symmetric groups, Internat. Math. Res. Notices, 2001, 4, pp. 179-192, (2001)
  • [2] Borodin A., CLT for spectra of submatrices of Wigner random matrices
  • [3] Borodin A., Ferrari P.L., Anisotropic growth of random surfaces in 2+1 dimensions
  • [4] Borodin A., Olshanski G., Reprentation theory and random point processes, European Congress of Mathematics, Eur. Math. Soc., Zürich, (2005)
  • [5] Borodin A., Olshanski G., Asymptotics of Plancherel-type random partions, J. Algebra, 313, 1, pp. 40-60, (2007)
  • [6] Cartier P., Introduction à l'étude des mouvements brownies à plusieurs paramètres, Séminaire De Probabilités (Strasbourg), 5, pp. 58-75, (1971)
  • [7] Meliot P.L., Kerov's central limit theorem for Schur Weyl measures of parameter 1/2
  • [8] Mkrtchyan S., Entropy of Schur Weyl measures
  • [9] Okounkov A., The uses of random partitions, XIVth International Congress on Mathmematical Physics, World Sci. Publ., pp. 379-403, (2005)
  • [10] Okounkov A., Olshanski G., Asymptotics of Jack polynomials as the number of variables goes to infinity, Internat. Math. Res. Notices, 1998, 13, pp. 641-682, (1988)