Point Processes and the Infinite Symmetric Group. Part II: Higher Correlation Functions

Simple item page
dc.creatorBorodin, Alexei
dc.date1998-04-18
dc.date.accessioned2026-07-07T05:24:26Z
dc.date.available2026-07-07T05:24:26Z
dc.descriptionWe continue the study of the correlation functions for the point stochastic processes introduced in Part I (G.Olshanski, math.RT/9804086). We find an integral representation of all the correlation functions and their explicit expression in terms of multivariate hypergeometric functions. Then we define a modification (``lifting'') of the processes which results in a substantial simplification of the structure of the correlation functions. It turns out that the ``lifted'' correlation functions are given by a determinantal formula involving a kernel. The latter has the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain Whittaker functions. Such a form for correlation functions is well known in the random matrix theory and mathematical physics. Finally, we get some asymptotic formulas for the correlation functions which are employed in Part III (A.Borodin and G.Olshanski, math.RT/9804088).
dc.descriptionAMSTeX, 57 pages
dc.identifierhttps://arxiv.org/abs/math/9804087
dc.identifierhttp://arxiv.org/abs/math/9804087
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76838
dc.subjectRepresentation Theory
dc.subjectCondensed Matter
dc.subjectHigh Energy Physics - Theory
dc.subjectProbability
dc.subjectExactly Solvable and Integrable Systems
dc.subject20C32, 15A52, 60G55
dc.titlePoint Processes and the Infinite Symmetric Group. Part II: Higher Correlation Functions
dc.typetext

Files

Collections

arXiv