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February 3, 2020 / Senya Shlosman (Skoltech, Aix Marseille Univ.) The Ising crystal and the Airy diffusion February 10, 2020 /Sergei Lando (Skoltech, HSE Univ.) Problems related to the weight system associated to the Lie algebra sl(2) February 17, 2020 / Alexandra Skripchenko (Skoltech, HSE Univ.) Interval exchange transformations with flips in dynamics and topology March 2, 2020 / Grigori Olshanski (Skoltech, IITP, HSE Univ.) Macdonald polynomials and discrete point processes March 16, 2020 / Michael Finkelberg (Skoltech, Univ. HSE) Geometric Satake correspondence and supergroups March 30, 2020 // Zoom / Igor Krichever (Skoltech, HSE Univ., Columbia Univ.) Algebraic integrability of 2D periodic elliptic sigma-models April 6, 2020 // Zoom / Alexander Braverman (Perimeter Inst, Univ of Toronto, Skoltech) Introduction to symplectic duality April 20, 2020 // Zoom / Vladimir Fock (Univ. of Strasbourg) Higher complex structures April 27, 2020 // Zoom / Alexander Veselov (Loughborough Univ., Moscow State Univ., Steklov Inst.) Automorphic Lie algebras and modular forms May 18, 2020 // Zoom / Davide Gaiotto (Perimeter Inst.) Protected operator algebras in three-dimensional supersymmetric quantum field theory May 25, 2020 // Zoom / Alexander Its (Indiana Univ.-Purdue Univ.) On the asymptotic analysis of the Calogero-Painlevé systems June 1, 2020 // Zoom / Konstantin Aleshkin (Columbia Univ.) Liouville quantum gravity and integrable systems June 8, 2020 // Zoom / Davide Gaiotto (Perimeter Inst.) Examples of boundary chiral algebras June 15, 2020 // Zoom / Alexandr Buryak (HSE Univ., Univ. of Leeds) Generalization of the Witten conjecture and non-commutative KdV system June 29, 2020 // Zoom / Gus Schrader (Columbia Univ.) An alternative functional realization of spherical DAHA |
July 13, 2020 // Zoom at 17.00
Mikhail Skvortsov, Nikolai Stepanov (Skoltech, Landau Inst.)
Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry
We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney’s problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half plane. We formulate the problem of statistical description of this never-falling trajectory and solve it by a field-theoretical technique assuming a white-noise driving. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistic properties of the never-falling trajectory are expressed in terms of the zero mode of the corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, which however is written for the “square root” of the probability distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of strong driving (no gravitation), we obtain an exact analytical solution for the instantaneous joint probability distribution function of the pendulum’s angle and its velocity
[ link to access the Seminar zoom.us/j/94069697919 ]