209 citations · 1.2k across the 68 of their papers we have counts for
8 papers · 1 filter
Macdonald-level extension of beta ensembles and large-N limit transition
Grigori Olshanski
We introduce and study a family of -deformed discrete -particle beta ensembles, where and are the parameters of Macdonald polynomials. The main result is the exis…
The Elliptic Tail Kernel
Cesar Cuenca, Vadim Gorin, Grigori Olshanski
We introduce and study a new family of -translation-invariant determinantal point processes on the two-sided -lattice. We prove that these processes are limits of the -$zw…
The ASEP and determinantal point processes
Alexei Borodin, Grigori Olshanski
We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for th…
Giambelli compatible point processes
Alexei Borodin, Grigori Olshanski, Eugene Strahov
We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of…
Markov processes on partitions
Alexei Borodin, Grigori Olshanski
We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic anal…
Stochastic dynamics related to Plancherel measure on partitions
Alexei Borodin, Grigori Olshanski
Consider the standard Poisson process in the first quadrant of the Euclidean plane, and for any point (u,v) of this quadrant take the Young diagram obtained by applying the Robinso…
Random partitions and the Gamma kernel
Alexei Borodin, Grigori Olshanski
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young dia…
Infinite random matrices and ergodic measures
Alexei Borodin, Grigori Olshanski
We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure fro…