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# Conditioned spectral density in ensembles of diluted random matrices (Isaac Perez Castillo – UNAM)

## 8 de março de 2018:15:00 - 16:00

Prof. Isaac Perez Castillo – National Autonomous University of Mexico (UNAM)

Data: 08/03/2018 as 15:00

Titulo: Conditioned spectral density in ensembles of diluted random matrices

Resumo: It has been very well established for some time now that, in the classical  Gaussian ensembles of random matrices, their spectral density conditioned to have a fraction of eigenvalues to the left of a wall at $x\in\mathbb{R}$ is: i) asymmetric; ii) has a non-compact support; iii) and it exhibits wetting of the eigenvalues at the wall,  all these features solely due to the Coulomb repulsion between eigenvalues. In this seminar, I present a novel method to obtain an analytical expression of the conditioned density on ensembles of diluted random matrices. For weighted random graphs we will see that its features are strikingly different the spectral density generally lies on a compact support, there is no wetting at the position of the wall, and it is always symmetric. Results are compared with Monte Carlo simulations showing fairly good agreement. We will end the discussion by pointing out that the method introduced is of a fairly general reach, and it can be used to derive “typical properties in atypical diluted systems”, both, in  and out-of-equilibrium.

## Detalhes

Data:
8 de março de 2018
Hora:
15:00 - 16:00
Categoria de Evento:

## Local

Anfiteatro Antônio Cabral (Prédio 43135, Sala 201)