相关论文: A note on the GFF with one free boundary condition
In this work, we investigate the continuity of the free boundary in a class of elliptic problems, with Neuman boundary condition. The main idea is a change of variable that allows us to reduce the problem to the one studied in [14].
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…
The problem of characterization of Gibbs random fields is considered. Various Gibbsianness criteria are obtained using the earlier developed one-point framework which in particular allows to describe random fields by means of either…
We consider both the infinite-volume discrete Gaussian Free Field (DGFF) and the DGFF with zero boundary conditions outside a finite box in dimension larger or equal to 3. We show that the associated extremal process converges to a Poisson…
We consider the effects of homogeneous Dirichlet's boundary conditions on two infinite parallel plane surfaces separated by a small distance {\it a}. We find that although spontaneous symmetry breaking does not occur for the theory of a…
We derive the existence of solutions for an asymptotically linear equation driven by the spectral fractional Laplacian operator with mixed Dirichlet-Neumann boundary conditions. When the nonlinear term $f$ is odd and a suitable relation…
In this paper we study some Schrodinger-Poisson type systems on a bounded domain, with Dirichlet boundary condition on both the variables.
We study a general class of elliptic free boundary problems equipped with a Dirichlet boundary condition. Our primary result establishes an optimal $C^{1,1}$-regularity estimate for $L^p$-strong solutions at points where the free and fixed…
We consider the Gaussian free field $\varphi$ on $\mathbb{Z}^d$ for $d \geq 3$ and study the level sets $\{\varphi \geq h \}$ in the percolating regime. We prove upper and lower bounds for the probability that the chemical distance is much…
We establish a martingale-type characterisations for the continuum Gaussian free field (GFF) and for fractional Gaussian free fields (FGFs), using their connection to the stochastic heat equation and to fractional stochastic heat equations.…
We show that there is "no stable free field of index $\alpha\in (1,2)$", in the following sense. It was proved in a previous work by the authors, that subject to a \emph{fourth moment assumption}, any random generalised function on a domain…
We derive an exact formula for the boundary free energy of the open Heisenberg XXZ spin chain. We allow for arbitrary boundary magnetic fields, but assume zero bulk magnetization. The result is completely analogous to earlier formulas for…
The dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a…
We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on…
We consider a generalized riffle shuffle on the colored permutation group $G_{p, n}$ and derive a determinantal formula for the probability of finding descents at given positions, proof of which is based on the bijection between the set of…
In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet-Neumann boundary data which extends the one proved by J. D\'avila to the fractional setting. In particular, we present a comparison…
We provide a concrete formula for a dual system as well as for a conjugate system of $q$-Gaussians represented on the $q$-deformed Fock space. Moreover, using this formula, we prove the existence of a free Gibbs potential and that the…
A multiple Gauss sum is a complete multiple exponential sum twisted by Dirichlet characters. We prove a new bound for multiple Gauss sums and, as an application, improve previous results in the Birch--Goldbach problem. Let $F_1, \ldots, F_R…
These lecture notes offer a gentle introduction to the two-dimensional Discrete Gaussian Free Field with particular attention paid to the scaling limits of the level sets at heights proportional to the absolute maximum. The bulk of the text…
We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we…