New methods to bound the critical probability in fractal percolation

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New methods to bound the critical probability in fractal percolation

The following full text is a preprint version which may differ from the publisher's version. Abstract: We study the critical probability p c (M) in two-dimensional M-adic fractal percolation. To find lower bounds, we compare fractal perco-lation with site percolation. Fundamentally new is the construction of an computable increasing sequence that converges to p c (M). We prove that p c (2) > 0....

متن کامل

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 ...

متن کامل

On the critical probability in percolation

For percolation on finite transitive graphs, Nachmias and Peres suggested a characterization of the critical probability based on the logarithmic derivative of the susceptibility. As a first test-case, we study their suggestion for the Erdős–Rényi random graph Gn,p, and confirm that the logarithmic derivative has the desired properties: (i) its maximizer lies inside the critical window p = 1/n+...

متن کامل

On the value of the critical point in fractal percolation

We derive a new lower bound p c > 0:8107 for the critical value of Mandelbrot's dyadic fractal percolation model. This is achieved by taking the random fractal set (to be denoted A 1) and adding to it a countable number of straight line segments, chosen in a certain (non-random) way as to simplify greatly the connectivity structure. We denote the modiied model thus obtained by C 1 , and write C...

متن کامل

Ja n 20 09 IS THE CRITICAL PERCOLATION PROBABILITY LOCAL ?

We show that the critical probability for percolation on a d-regular nonamenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. This is a special case of a conjecture due to O. Schramm on the locality of pc. We also prove a finite analogue of the conjecture for expander graphs.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Random Structures & Algorithms

سال: 2014

ISSN: 1042-9832

DOI: 10.1002/rsa.20566