271 citations · 649 across the 16 of their papers we have counts for
7 papers · 1 filter
Limits of determinantal processes near a tacnode
Alexei Borodin, Maurice Duits
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter $\eps> 0$. The domain has two cusps, one poin…
On adding a list of numbers (and other one-dependent determinantal processes)
Alexei Borodin, Persi Diaconis, Jason Fulman
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-d…
Infinite-dimensional diffusions as limits of random walks on partitions
Alexei Borodin, Grigori Olshanski
The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group. This problem leads to a family {P_z} of probability measur…
Asymptotics of Plancherel-type random partitions
Alexei Borodin, Grigori Olshanski
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, t…
Meixner polynomials and random partitions
Alexei Borodin, Grigori Olshanski
The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of ha…
Loop-free Markov chains as determinantal point processes
Alexei Borodin
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of par…