61 citations · 297 across the 23 of their papers we have counts for
11 papers · 1 filter
Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product
Mufan Li, Jaume de Dios Pont, Mihai Nica +1
We study the squared singular value spectrum of a non-square product of independent real Gaussian matrices, equivalently the feature covariance spectrum of a deep linear neural net…
RSK in last passage percolation: a unified approach
Duncan Dauvergne, Mihai Nica, Bálint Virág
We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show t…
One-sided reflected Brownian motions and the KPZ fixed point
Mihai Nica, Jeremy Quastel, Daniel Remenik
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition pro…
Uniform convergence to the Airy line ensemble
Duncan Dauvergne, Mihai Nica, Bálint Virág
We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our…
Solution of the Kolmogorov equation for TASEP
Mihai Nica, Jeremy Quastel, Daniel Remenik
We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov back…
Products of Many Large Random Matrices and Gradients in Deep Neural Networks
Boris Hanin, Mihai Nica
We study products of random matrices in the regime where the number of terms and the size of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of…
Intermediate disorder limits for multi-layer semi-discrete directed polymers
Mihai Nica
We show that the partition function of the multi-layer semi-discrete directed polymer converges in the intermediate disorder regime to the partition function for the multi-layer co…
Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
Ivan Corwin, Mihai Nica
We consider directed polymer models involving multiple non-intersecting random walks moving through a space-time disordered environment in one spatial dimension. For a single rando…
Optimal Strategy in "Guess Who?": Beyond Binary Search
Mihai Nica
"Guess Who?" is a popular two player game where players ask "Yes"/"No" questions to search for their opponent's secret identity from a pool of possible candidates. This is modeled…
Decorated Young Tableaux and the Poissonized Robinson-Schensted Process
Mihai Nica
We introduce an object called a decorated Young tableau which can equivalently be viewed as a continuous time trajectory of Young diagrams or as a non-intersecting line ensemble. B…
Stabilization Time for a Type of Evolution on Binary Strings
Jacob Funk, Mihai Nica, Michael Noyes
We consider a type of evolution on {0,1}^n which occurs in discrete steps whereby at each step, we replace every occurrence of the substring "01" by "10". After at most n-1 steps w…