209 citations · 1.2k across the 68 of their papers we have counts for
4 papers · 2 filters
The quasi-invariance property for the Gamma kernel determinantal measure
Grigori Olshanski
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 Gamma fu…
-exchangeability via quasi-invariance
Alexander Gnedin, Grigori Olshanski
For positive , the -exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for…
A q-analogue of de Finetti's theorem
Alexander Gnedin, Grigori Olshanski
A q-analogue of de Finetti's theorem is obtained in terms of a boundary problem for the q-Pascal graph. For q a power of prime this leads to a characterisation of random spaces ove…
Anisotropic Young diagrams and infinite-dimensional diffusion processes with the Jack parameter
Grigori Olshanski
We construct a family of Markov processes with continuous sample trajectories on an infinite-dimensional space, the Thoma simplex. The family depends on three continuous parameters…