14 citations · 37 across the 5 of their papers we have counts for
9 papers
Differential equations for the KPZ and periodic KPZ fixed points
Jinho Baik, Andrei Prokhorov, Guilherme L. F. Silva
The KPZ fixed point is a 2d random field, conjectured to be the universal limiting fluctuation field for the height function of models in the KPZ universality class. Similarly, the…
Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation
Promit Ghosal, Guilherme L. F. Silva
We study multiplicative statistics for the eigenvalues of unitarily-invariant Hermitian random matrix models. We consider one-cut regular polynomial potentials and a large class of…
Large n limit for the product of two coupled random matrices
Guilherme L. F. Silva, Lun Zhang
For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean…
Spectral curves, variational problems and the hermitian matrix model with external source
Andrei Martínez-Finkelshtein, Guilherme L. F. Silva
We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All su…
Supercritical Regime for the Kissing Polynomials
Andrew F. Celsus, Guilherme L. F. Silva
We study a family of polynomials which are orthogonal with respect to the varying, highly oscillatory complex weight function on , where is a positive parame…
Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight
Andrei Martínez-Finkelshtein, Guilherme Silva
We consider the type I multiple orthogonal polynomials (MOPs) and type II MOPs , satisfying non-hermitian orthogonality with respect to the weight $e^…
The mother body phase transition in the normal matrix model
Pavel Bleher, Guilherme Silva
The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, invers…
Critical measures for vector energy: global structure of trajectories of quadratic differentials
Andrei Martinez-Finkelshtein, Guilherme Silva
Saddle points of a vector logarithmic energy with a vector polynomial external field on the plane constitute the vector critical measures, a notion that finds a natural motivation…
S-curves in Polynomial External Fields
Arno Kuijlaars, Guilherme Silva
Curves in the complex plane that satisfy the S-property were first introduced by Stahl and they were further studied by Gonchar and Rakhmanov in the 1980s. Rakhmanov recently showe…