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Proof of the exact diffusion constant via first passage time in quasi-periodic potentials
Ming Gong
https://arxiv.org/abs/2510.10435 https://arxiv.org/pdf/…

Proof of the exact diffusion constant via first passage time in quasi-periodic potentials
Brownian motion in terms of Lifson and Jackson (LJ) formula has been widely explored in periodic systems and it has been believed for a long time that the LJ formula only applies to periodic potentials. Recently we show that for the following Brownian motion $γ\dot{x} = -U'(x) + ξ$, where $U(x)$ is the quasi-periodic potential, the effective diffusion constant can still be described by the LJ formula $D^* = D/(\langle \exp(βU)\rangle \langle \exp(-βU)\rangle)$, where the average is redefine…

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A class of Truncated Freud polynomials
Juan Carlos Garc\'ia-Ardila, Francisco Marcell\'an, Misael E. Marriaga
https://arxiv.org/abs/2510.09214 https://

A class of Truncated Freud polynomials
Consider the following truncated Freud linear functional $\mathbf{u}_z$ depending on a parameter $z$, $$\langle\mathbf{u}_z,p\rangle=\int_0^\infty p(x)e^{-zx^4}dx,\quad z>0.$$ The aim of this work is to analyze the properties of the sequence of orthogonal polynomials $(P_n)_{n\geq 0}$ with respect to $\mathbf{u}_z$. Such a linear functional is semiclassical and, as a consequence, we get the system of nonlinear difference equations (Laguerre-Freud equations) that the coefficients of the three-te…