Values of Brownian intersection exponents, II: Plane exponents
نویسندگان
چکیده
منابع مشابه
Values of Brownian intersection exponents II: Plane exponents
We derive the exact value of intersection exponents between planar Brownian motions or random walks, confirming predictions from theoretical physics by Duplantier and Kwon. Let B and B′ be independent Brownian motions (or simple random walks) in the plane, started from distinct points. We prove that the probability that the paths B[0, t] and B′[0, t] do not intersect decays like t−5/8. More pre...
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This paper proves conjectures originating in the physics literature regarding the intersection exponents of Brownian motion in a halfplane. For instance, suppose that B and B′ are two independent planar Brownian motions started from distinct points in a half-plane H. Then as t → ∞,
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This paper determines values of intersection exponents between packs of planar Brownian motions in the half-plane and in the plane that were not derived in our first two papers. For instance, it is proven that the exponent ξ(3, 3) describing the asymptotic decay of the probability of nonintersection between two packs of three independent planar Brownian motions each is (73 − 2 √ 73)/12. More ge...
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Let p ≥ 2, n1 ≤ · · · ≤ np be positive integers and B 1 , . . . , B n1 ; . . . ;B p 1 , . . . , B np be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ςp(n1, . . . , np), as the exponential rate of decay of the probability that the packets ⋃ni j=1 B i j [0, t ], i = 1, . . . , p, have no joint intersection. The ...
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We derive properties concerning all intersection exponents for planar Brownian motion and we deene generalized exponents that loosely speaking correspond to non-integer numbers of Brownian paths. Some of these properties lead to general conjectures concerning the exact value of these exponents.
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2001
ISSN: 0001-5962
DOI: 10.1007/bf02392619