Multi angle Tilings and non-intersecting paths beyond integrable cases
Auteurs : Gorin, Vadim (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : The talk is about a class of systems of 2d statistical mechanics, such as random tilings, noncolliding walks, log-gases and random matrix-type distributions. Specific members in this class are integrable, which means that available exact formulas allow delicate asymptotic analysis leading to the Gaussian Free Field, sine-process, Tracy-Widom distributions. Extending the results beyond the integrable cases is challenging. I will speak about a recent progress in this direction: about universal local limit theorems for a class of lozenge and domino tilings, noncolliding random walks; and about GFF-type asymptotic theorems for global fluctuations in these systems and in discrete beta loggases.Codes MSC :
52C20 - Tilings in $2$ dimensions
60C05 - Combinatorial probability
60G50 - Sums of independent random variables; random walks