اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNo repulsion between critical points for planar Gaussian random fields
152
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal. Our main result implies that for a generic field the critical points neither repel nor attract each other. Our analysis also allows to study how the short-range behaviour of critical points depends on their index.
قيم البحث
اقرأ أيضاً
Let a<b, Omega=[a,b]^{Z^d} and H be the (formal) Hamiltonian defined on Omega by H(eta) = frac12 sum_{x,yinZ^d} J(x-y) (eta(x)-eta(y))^2 where J:Z^dtoR is any summable non-negative symmetric function (J(x)ge 0 for all xinZ^d, sum_x J(x)<infty and J
(x)=J(-x)). We prove that there is a unique Gibbs measure on Omega associated to H. The result is a consequence of the fact that the corresponding Gibbs sampler is attractive and has a unique invariant measure.
Given a sequence of lattice approximations $D_Nsubsetmathbb Z^2$ of a bounded continuum domain $Dsubsetmathbb R^2$ with the vertices outside $D_N$ fused together into one boundary vertex $varrho$, we consider discrete-time simple random walks in $D_N
cup{varrho}$ run for a time proportional to the expected cover time and describe the scaling limit of the exceptional level sets of the thick, thin, light and avoided points. We show that these are distributed, up a spatially-dependent log-normal factor, as the zero-average Liouville Quantum Gravity measures in $D$. The limit law of the local time configuration at, and nearby, the exceptional points is determined as well. The results extend earlier work by the first two authors who analyzed the continuous-time problem in the parametrization by the local time at $varrho$. A novel uniqueness result concerning divisible random measures and, in particular, Gaussian Multiplicative Chaos, is derived as part of the proofs.
This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The
result is applicable to fractional Brownian sheets and the solutions of systems of stochastic heat and wave equations.
We consider Activated Random Walks on $Z$ with totally asymmetric jumps and critical particle density, with different time scales for the progressive release of particles and the dissipation dynamics. We show that the cumulative flow of particles thr
ough the origin rescales to a pure-jump self-similar process which we describe explicitly.
We consider symmetric activated random walks on $mathbb{Z}$, and show that the critical density $zeta_c$ satisfies $csqrt{lambda} leq zeta_c(lambda) leq C sqrt{lambda}$ where $lambda$ denotes the sleep rate.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
