TY - BOOK
T1 - Analyticity Results in Bernoulli Percolation
AU - Georgakopoulos, Agelos
AU - Panagiotis, Christoforos
PY - 2023/8/3
Y1 - 2023/8/3
N2 - We prove that for Bernoulli percolation on Zd, d ≥ 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 short- or long-range models, and that pbond c < 1/2 for certain families of triangulations for which Benjamini & Schramm conjectured that psite c ≤ 1/2.
AB - We prove that for Bernoulli percolation on Zd, d ≥ 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 short- or long-range models, and that pbond c < 1/2 for certain families of triangulations for which Benjamini & Schramm conjectured that psite c ≤ 1/2.
UR - http://www.scopus.com/inward/record.url?scp=85173962179&partnerID=8YFLogxK
U2 - 10.1090/MEMO/1431
DO - 10.1090/MEMO/1431
M3 - Book
SN - 9781470467050
T3 - Memoirs of the American Mathematical Society
BT - Analyticity Results in Bernoulli Percolation
PB - American Mathematical Society
CY - U. S. A.
ER -
