|
|
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
|
Number of views: |
This page: | 183 |
|
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.
|
|