Details

Subject(s)

• Percolation (Statistical physics) [Browse]
• Combinatorial enumeration problems [Browse]
• Probabilities [Browse]
• Mathematical physics [Browse]
• Combinatorial analysis [Browse]

Author

• Panagiotis, Christoforos [Browse]

Series

Memoirs of the American Mathematical Society ; no. 1431. [More in this series]

Summary note

"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.

Bibliographic references

Includes bibliographical references.

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.

Show 13 more Contents items

ISBN

• 9781470467050 ((paperback))
• 1470467054

LCCN

2023056195

OCLC

1395536631

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