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LARGE DEVIATION PRINCIPLE FOR THE ABLOWITZ-LADIK LATTICE AND THE CIRCULAR β ENSEMBLE AT HIGH TEMPERATURE

Speaker: 
Guido Mazzuca
Institution: 
KTH, Sweden
Schedule: 
Wednesday, June 7, 2023 - 16:00
Location: 
A-132
Abstract: 

This presentation delves into the fascinating relationship between integrable systems theory and random matrix theory. In particular, a method to calculate the eigenvalue density of the Lax matrix   of the Ablowitz-Ladik lattice   sampled from the  Generalized Gibbs ensemble is derived.  This characterization is achieved by employing a large deviation principle (LDP). Additionally,  a connection between this LDP and the one of the Circular β ensemble in the high temperature regime is established. This permits to  explicitly compute the eigenvalue density of the Ablowitz-Ladik lattice random Lax matrix. 

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