90 citations · 357 across the 29 of their papers we have counts for
4 papers · 1 filter
Integrable probability: From representation theory to Macdonald processes
Alexei Borodin, Leonid Petrov
These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic…
Spectral theory for the q-Boson particle system
Alexei Borodin, Ivan Corwin, Leonid Petrov +1
We develop spectral theory for the generator of the q-Boson (stochastic) particle system. Our central result is a Plancherel type isomorphism theorem for this system. This theorem…
The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension
Ivan Corwin, Leonid Petrov
We introduce a new interacting (stochastic) particle system q-PushASEP which interpolates between the q-TASEP introduced by Borodin and Corwin (see arXiv:1111.4408, and also arXiv:…
Nearest neighbor Markov dynamics on Macdonald processes
Alexei Borodin, Leonid Petrov
Macdonald processes are certain probability measures on two-dimensional arrays of interlacing particles introduced by Borodin and Corwin (arXiv:1111.4408 [math.PR]). They are defin…