A lower bound for point-to-point connection probabilities in critical percolation

Upper transition point for percolation on the enhanced binary tree: a sharpened lower bound.

Hyperbolic structures are obtained by tiling a hyperbolic surface with negative Gaussian curvature. These structures generally exhibit two percolation transitions: a system-wide connection can be established at a certain occupation probability p = pc1, and there emerges a unique giant cluster at pc2 > pc1. There have been debates about locating the upper transition point of a prototypical hyper...

Percolation systems away from the critical point

This article reviews some effects of disorder in percolation systems away from the critical density pc. For densities below pc, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee–Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singularities in the free energy of diluted ferromagnets, and...

fixed point property for banach algebras associated to locally compact groups

در این پایان نامه به بررسی خاصیت نقطه ثابت و خاصیت نقطه ثابت برای نیم گروههای برگشت پذیر چپ روی بعضی جبرهای باناخ از جمله جبر فوریه و جبر فوریه استیلتیس پرداخته شده است. برای مثال بیان شده است که اگر گروه یک گروه فشرده موضعی با همسایگی فشرده برای عنصر همانی که تحت درونریختی ها پایاست باشد آنگاه جبر فوریه و جبر فوریه استیلتیس دارای خاصیت نقطه ثابت برای نیم گروه های برگشت پذیر چپ است اگر و تنها ا...

New Lower Bound on the Critical Density in Continuum Percolation

Percolation theory has become a useful tool for the analysis of large scale wireless networks. We investigate the fundamental problem of characterizing the critical density λc for Poisson random geometric graphs in continuum percolation theory. In two-dimensional space with the Euclidean norm, simulation studies show λc ≈ 1.44, while the best theoretical bounds obtained thus far are 0.696 < λc ...

A Better Lower Bound for Two-Circle Point Labeling