Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Arm exponents in high dimensional percolation
HTML articles powered by AMS MathViewer

by Gady Kozma and Asaf Nachmias
J. Amer. Math. Soc. 24 (2011), 375-409
DOI: https://doi.org/10.1090/S0894-0347-2010-00684-4
Published electronically: November 16, 2010

Abstract:

We study the probability that the origin is connected to the sphere of radius $r$ (an arm event) in critical percolation in high dimensions, namely when the dimension $d$ is large enough or when $d>6$ and the lattice is sufficiently spread out. We prove that this probability decays like $r^{-2}$. Furthermore, we show that the probability of having $\ell$ disjoint arms to distance $r$ emanating from the vicinity of the origin is $r^{-2\ell }$.
References
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 60K35, 82B43
  • Retrieve articles in all journals with MSC (2010): 60K35, 82B43
Bibliographic Information
  • Gady Kozma
  • Affiliation: The Weizmann Institute of Science, Rehovot POB 76100, Israel
  • MR Author ID: 321409
  • Email: gady.kozma@weizmann.ac.il
  • Asaf Nachmias
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • Email: asafnach@math.mit.edu
  • Received by editor(s): November 4, 2009
  • Received by editor(s) in revised form: July 21, 2010
  • Published electronically: November 16, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 24 (2011), 375-409
  • MSC (2010): Primary 60K35, 82B43
  • DOI: https://doi.org/10.1090/S0894-0347-2010-00684-4
  • MathSciNet review: 2748397