Further Asymptotic Laws of Planar Brownian Motion
نویسندگان
چکیده
منابع مشابه
Logarithmic Potentials and Planar Brownian Motion
In Section 5, we saw that for a Brownian motion process in n _ 3 dimensions, P (limtxIX, = o0) = 1 for all x. In sharp contrast to this situation, a planar Brownian motion is certain to hit any nonpolar set. THEOREM 8.1. Let B be a Borel set. Then PX(VB < cX) is either identically 1 or identically 0. PROOF. A simple computation shows that for any x e R2, 1' p(s, x) ds T co as t T oc. Thus, for ...
متن کاملMultiple intersection exponents for planar Brownian motion
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 ...
متن کاملIntersection Exponents for Planar Brownian Motion
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.
متن کاملConditioned Brownian motion in planar domains
We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains. Short title: Conditioned Brownian motion AMS Subject Classification (1985): Primary 60J50; Secondary 60J45, 60J65
متن کاملAsymptotic Enumeration and Limit Laws of Planar Graphs
A graph is planar if it can be embedded in the plane, or in the sphere, so that no two edges cross at an interior point. A planar graph together with a particular embedding is called a map. There is a rich theory of counting maps, started by Tutte in the 1960’s. However, in this paper we are interested in counting graphs as combinatorial objects, regardless of how many nonequivalent topological...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1989
ISSN: 0091-1798
DOI: 10.1214/aop/1176991253