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Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
March 21, 2018 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)
 


Combinatorics of paths on super-trees with applications in statistical physics and field theory

A. S. Gorskya, S. K. Nechaevbc

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Interdisciplinary Scientific Center J.-V.Poncelet
c P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow

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Abstract: In the talk we consider the spectral properties of transfer-matrices on "super-trees" (trees whose vertex degree varies with the distance from the root point). At small "branching rates", the path combinatorics on super-trees coincides with the statistics of one-dimensional Dyck paths weighted with the area under the trajectory. We discuss the relationship of statistics on super-trees with the Kardar-Parisi-Zhang statistics, the one-dimensional Anderson localization, and the random matrix theory in the Edelman-Dumitru representation. Trees with variable branching also encode the structure of some Fock space. Random walk on super-trees is a specific example of statistical model related to CFT, on the one hand, and ODE spectral properties, known as ODE/IS correspondence, on the other hand.

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