Longest increasing subsequences of random colored permutations.
Harmonic functions on multiplicative graphs and interpolation polynomials.
Large time asymptotics of growth models on space-like paths. I: Push ASEP.
Loop-free Markov chains as determinantal point processes
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 particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
Maximum of Dyson Brownian motion and non-colliding systems with a boundary.
Limits of determinantal processes near a tacnode
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process....
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