Journal of Mathematical Sciences

, Volume 238, Issue 6, pp 769–778 | Cite as

Continuous-Time Multidimensional Walks as an Integrable Model

  • N. BogoliubovEmail author

We consider continuous-time random walks on multidimensional symplectic lattices. It is shown that the generating functions of random walks and the transition amplitudes of continuous-time quantum walks can be expressed through dynamical correlation functions of an exactly solvable model describing strongly correlated bosons on a chain, the so-called phase model. The number of random lattice paths with a fixed number of steps connecting the starting and ending points on the multidimensional lattice is expressed through solutions of the Bethe equations of the phase model. Its asymptotics is obtained in the limit of a large number of steps.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St.Petersburg Department of Steklov Institute of MathematicsITMO UniversitySt.PetersburgRussia

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