Spectral theory for the q-Boson particle system
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.
The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension
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:1207.5035; arXiv:1305.2972; arXiv:1212.6716) and the $q$-PushTASEP introduced recently by Borodin and Petrov (arXiv:1305.5501).
Markov Dynamics on Interlacing Arrays
The talk is devoted to the construction of Markov dynamics on interlacing arrays which act nicely on the Macdonald measures. In a particular case one gets $q$-deformed Robinson-Schensted insertion algorithms. The talk is based on [12], [13], see also [14], [15].
Nearest neighbor Markov dynamics on Macdonald processes
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 defined in terms of nonnegative specializations of the Macdonald symmetric functions and depend on two parameters $(q,t)$, where $0\le q, t < 1$. Our main result is a classification of continuous time, nearest neighbor Markov dynamics on the space of interlacing arrays that act nicely on Macdonald processes.
MATH 4581 • Statistics and Stochastic Processes
MATH 7382 • Representation theory of big groups and probability (Graduate topics course)
Syllabus • Lecture Notes • updated: 2011/15/12
MATH 1342 • Calculus II for Sci&Eng, Honors
The Boundary of the Gelfand-Tsetlin Graph: New Proof of Borodin-Olshanski's Formula, and its q-analogue
In the recent paper [arXiv:1109.1412], Borodin and Olshanski have presented a novel proof of the celebrated Edrei-Voiculescu theorem which describes the boundary of the Gelfand-Tsetlin graph as a region in an infinite-dimensional coordinate space.