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 کاملFluctuation of planar Brownian loop capturing large area
Abstract. We consider a planar Brownian loop B that is run for a time T and conditioned on the event that its range encloses the unusually high area of πT 2, with T ∈ (0,∞) being large. We study the deviation of the range of the conditioned process X from a circle of radius T , as a model for the fluctuation of a phase boundary. This deviation is measured by the inradius Rin(X) and outradius Ro...
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: Communications in Mathematical Physics
سال: 2011
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-011-1234-9