Lower bounds for boundary roughness for droplets in Bernoulli percolation

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dc.creatorUzun, Hasan B.
dc.creatorAlexander, Kenneth S.
dc.date2002-10-01
dc.date.accessioned2026-07-07T04:51:25Z
dc.date.available2026-07-07T04:51:25Z
dc.descriptionWe consider boundary roughness for the ``droplet'' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least $l^2$, for large $l$. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large $l$ this maximum is at least of order $l^{1/3}(\log l)^{-2/3}$. This complements the upper bound of order $l^{1/3}(\log l)^{2/3}$ known for the average local roughness. The exponent 1/3 on $l$ here is in keeping with predictions from the physics literature for interfaces in two dimensions.
dc.description28 pages, 1 figure (.eps file). See also http://math.usc.edu/~alexandr/
dc.identifierhttps://arxiv.org/abs/math/0210016
dc.identifierhttp://arxiv.org/abs/math/0210016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65139
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B20, 82B43
dc.titleLower bounds for boundary roughness for droplets in Bernoulli percolation
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