CaltechAUTHORS
  A Caltech Library Service

Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on ℤᵈ

Hutchcroft, Tom (2022) Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on ℤᵈ. Journal of Mathematical Physics, 63 (11). Art. No. 113301. ISSN 0022-2488. doi:10.1063/5.0088450. https://resolver.caltech.edu/CaltechAUTHORS:20221129-370786800.2

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20221129-370786800.2

Abstract

Consider long-range Bernoulli percolation on ℤᵈ in which we connect each pair of distinct points x and y by an edge with probability 1 − exp(−β‖x − y‖^(−d−α)), where α > 0 is fixed and β ⩾ 0 is a parameter. We prove that if 0 < α < d, then the critical two-point function satisfies (1/|Λ_r|)∑_(xϵΛ_(r))P_(β_(c))(0 ↔ x) ≤ r^(−d+a) for every r ⩾ 1, where Λ_r = [−r,r]ᵈ ∩ ℤᵈ. In other words, the critical two-point function on ℤᵈ is always bounded above on average by the critical two-point function on the hierarchical lattice. This upper bound is believed to be sharp for values of α strictly below the crossover value α_(c)(d), where the values of several critical exponents for long-range percolation on ℤᵈ and the hierarchical lattice are believed to be equal.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/5.0088450DOIArticle
ORCID:
AuthorORCID
Hutchcroft, Tom0000-0003-0061-593X
Additional Information:We thank Philip Easo, Emmanuel Michta, Gordon Slade, and the anonymous referee for helpful comments on earlier versions of the manuscript.
Issue or Number:11
DOI:10.1063/5.0088450
Record Number:CaltechAUTHORS:20221129-370786800.2
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20221129-370786800.2
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118141
Collection:CaltechAUTHORS
Deposited By: Research Services Depository
Deposited On:22 Dec 2022 16:59
Last Modified:22 Dec 2022 16:59

Repository Staff Only: item control page