اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAsymptotics for Lipschitz percolation above tilted planes
48
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider Lipschitz percolation in $d+1$ dimensions above planes tilted by an angle $gamma$ along one or several coordinate axes. In particular, we are interested in the asymptotics of the critical probability as $d to infty$ as well as $gamma to pi/4.$ Our principal results show that the convergence of the critical probability to 1 is polynomial as $dto infty$ and $gamma to pi/4.$ In addition, we identify the correct order of this polynomial convergence and in $d=1$ we also obtain the correct prefactor.
قيم البحث
اقرأ أيضاً
In this paper, we consider Strassens version of optimal transport (OT) problem. That is, we minimize the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given distributions. We deri
ve large deviation, moderate deviation, and central limit theorems for this problem. Our proof is based on Strassens dual formulation of the OT problem, Sanovs theorem on the large deviation principle (LDP) of empirical measures, as well as the moderate deviation principle (MDP) and central limit theorems (CLT) of empirical measures. In order to apply the LDP, MDP, and CLT to Strassens OT problem, two nested optimal transport formulas for Strassens OT problem are derived. Based on these nested formulas and using a splitting technique, we carefully design asymptotically optimal solutions to Strassens OT problem and its dual formulation.
We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a fixed interval is given by $e^{-frac{beta}{2} n^2 log(n)+O(n^2)}$ as $
nto infty$. We also identify the next order term in the exponent if the size of the interval goes to zero.
We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct application of a classical theorem due to Bobkov and G{o}tze.
This paper numerically investigates the feasibility of lensless zoomable holographic multiple projections to tilted planes. We have already developed lensless zoomable holographic single projection using scaled diffraction, which calculates diffracti
on between parallel planes with different sampling pitches. The structure of this zoomable holographic projection is very simple because it does not need a lens; however, it only projects a single image to a plane parallel to the hologram. The lensless zoomable holographic projection in this paper is capable of projecting multiple images onto tilted planes simultaneously.
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on ${
mathbb Z}^d$ with parameter $pin (0,1]$. For each occupied site $v$, and for each of the $2d$ possible coordinate directions, declare the entire line segment from $v$ to the next occupied site in the given direction to be either blue or not blue according to a given stochastic rule. In the one-choice model, each occupied site declares one of its $2d$ incident segments to be blue. In the independent model, the states of different line segments are independent.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
