Abstract:
An adjacency operator on a group is a formal sum of (left) regular representations over a conjugacy class. For such adjacency operators on the infinite symmetric group which are parametrized by the Young diagrams, we discuss the correlation of their powers with respect to the vacuum vector state. We compute exactly the correlation function under suitable normalization and through the infinite volume limit. This approach is viewed as a central limit theorem in quantum probability, where the operators are interpreted as random variables via spectral decomposition. In [K], Kerov showed the corresponding result for one-row Young diagrams. Our formula provides an extension of Kerov's theorem to the case of arbitrary Young diagrams.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 16 October 1997 / Accepted: 29 November 1997
Rights and permissions
About this article
Cite this article
Hora, A. Central Limit Theorem for the Adjacency Operators on the Infinite Symmetric Group . Comm Math Phys 195, 405–416 (1998). https://doi.org/10.1007/s002200050395
Issue Date:
DOI: https://doi.org/10.1007/s002200050395