The quasi-invariance property for the Gamma kernel determinantal measure

Результат исследований: Вклад в журналСтатьярецензирование

20 Цитирования (Scopus)

Аннотация

The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Γ-function. The Gamma kernel depends on two continuous parameters; its principal minors serve as the correlation functions of a determinantal probability measure P defined on the space of infinite point configurations on the lattice. As was shown earlier [A. Borodin, G. Olshanski, Adv. Math. 194 (2005) 141-202, arXiv:math-ph/0305043], P describes the asymptotics of certain ensembles of random partitions in a limit regime.Theorem: The determinantal measure P is quasi-invariant with respect to finitary permutations of the nodes of the lattice.This result is motivated by an application to a model of infinite particle stochastic dynamics.

Язык оригиналаАнглийский
Страницы (с-по)2305-2350
Число страниц46
ЖурналAdvances in Mathematics
Том226
Номер выпуска3
DOI
СостояниеОпубликовано - 15 февр. 2011
Опубликовано для внешнего пользованияДа

Fingerprint

Подробные сведения о темах исследования «The quasi-invariance property for the Gamma kernel determinantal measure». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать