Analyticity results in Bernoulli percolation / Agelos Georgakopoulos, Christoforos Panagiotis.

Format:

Book

Author/Creator:

Georgakopoulos, Agelos, author.

Panagiotis, Christoforos, author.

Series:

Memoirs of the American Mathematical Society ; no. 1431.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1431.

Language:

English

Subjects (All):

Percolation (Statistical physics).

Combinatorial enumeration problems.

Probabilities.

Mathematical physics.

Combinatorial analysis.

probability.

Physical Description:

v, 102 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"We prove that for Bernoulli percolation on Zd, d (greater than or equal to) 2, the percolation density is an analytic function of the parameter in the supercritical interval. For this we introduce some techniques that have further implications. In particular, we prove that the susceptibility is analytic in the subcritical interval for all transitive shortor long-range models, and that pbond c (less than) 1/2 for certain families of triangulations for which Benjamini & Schramm conjectured that psite c (less than or equal to) 1/2"-- Provided by publisher.

Contents:

Chapter 1. Introduction

Chapter 2. The setup

Chapter 3. Definitions and preliminaries

Chapter 4. The basic technique

Chapter 5. Analyticity for non-amenable groups

Chapter 6. Trees

Chapter 7. Analyticity above the threshold for planar lattices

Chapter 8. Analyticity of percolation density in all dimensions

Chapter 9. Continuum percolation

Chapter 10. Finitely presented groups

Chapter 11. Triangulations

Chapter 12. Alternating signs of Taylor coefficients

Chapter 13. The negative percolation threshold

Appendix A. On the number of lattice animals of a given size

Appendix B. Complex analysis basics

Bibliography.

Notes:

Includes bibliographical references.

ISBN:

9781470467050

1470467054

OCLC:

1395536631