Exact Persistence Exponent for the 2 D -Diffusion Equation and Related Kac Polynomials

We compute the persistence for the $2d$-diffusion equation with random initial condition, i.e., the probability $p_0(t)$ that the diffusion field, at a given point ${\bf x}$ in the plane, has not changed sign up to time $t$. For large $t$, we show that $p_0(t) \sim t^{-\theta(2)}$ with $\theta(2) =...

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Veröffentlicht in:	Physical review letters 2018-10, Vol.121 (15), Article 150601
Hauptverfasser:	Poplavskyi, Mihail, Schehr, Grégory
Format:	Artikel
Sprache:	eng
Schlagworte:	Condensed Matter Mathematical Physics Mathematics Physics Probability Statistical Mechanics
Online-Zugang:	Volltext
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