Výsledky vyhledávání - "Piatnitski, A L"

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On spectra of convolution operators with potentials

Autor: Borisov, Denis I., Piatnitski, Andrey L., Zhizhina, Elena A.

This paper focuses on the spectral properties of a bounded self-adjoint operator in $L_2(\mathds R^d)$ being the sum of a convolution operator with an integrable convolution kernel and an operator of multiplication by a continuous potential convergin

Externí odkaz: http://arxiv.org/abs/2201.04511

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Akademický článek

Spectrum of One-Dimensional Potential Perturbed by a Small Convolution Operator: General Structure.

Autor: Borisov, D. I.¹ (AUTHOR) borisovdi@yandex.ru, Piatnitski, A. L.^2,3 (AUTHOR) apiatnitski@gmail.com, Zhizhina, E. A.^2,3 (AUTHOR) ejj@iitp.ru

Publikováno v: Mathematics (2227-7390). Oct2023, Vol. 11 Issue 19, p4042. 26p.

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Khasminskii--Whitham averaging for randomly perturbed KdV equation

Autor: Kuksin, Sergei B., Piatnitski, Andrey L.

We consider the damped-driven KdV equation $$ \dot u-\nu{u_{xx}}+u_{xxx}-6uu_x=\sqrt\nu \eta(t,x), x\in S^1, \int u dx\equiv \int\eta dx\equiv0, $$ where $0<\nu\le1$ and the random process $\eta$ is smooth in $x$ and white in $t$. For any periodic fu

Externí odkaz: http://arxiv.org/abs/0710.3869

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Quenched invariance principles for random walks on percolation clusters

Autor: Mathieu, P., Piatnitski, A. L.

Publikováno v: Proceedings A of the Royal Society, vol. 463, 2287-2307, 2007

We prove the almost sure ('quenched') invariance principle for a random walker on an infinite Bernoulli percolation cluster in $\Z^d$ where $d$ is larger or equal than 2.
Comment: Different and more self-contained exposition of the main step of

Externí odkaz: http://arxiv.org/abs/math/0505672

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