NONINTERSECTION EXPONENTS FOR BROWNIAN PATHS .1. EXISTENCE AND AN INVARIANCE-PRINCIPLE

被引：25

作者：

BURDZY, K ^{[1
]}

LAWLER, GF ^{[1
]}

机构：

[1] DUKE UNIV,DEPT MATH,DURHAM,NC 27706

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1990年 / 84卷 / 03期

关键词：

D O I：

10.1007/BF01197892

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let X and Y be independent 3-dimensional Brownian motions, X(0)=(0,0,0), Y(0)=(1,0,0) and let pr=P(X[0, r] {n-ary intersection}Y[0, r]=∅). Then the "non-intersection exponent" {Mathematical expression} exists and is equal to a similar "non-intersection exponent" for random walks. Analogous results hold in R2 and for more than 2 paths. © 1990 Springer-Verlag.

引用

页码：393 / 410

页数：18

共 13 条

[1] GEOMETRIC ANALYSIS OF PHI-4 FIELDS AND ISING-MODELS .1.2. [J].

AIZENMAN, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 86 (01) :1-48

[2] ON THE CRITICAL EXPONENT FOR RANDOM-WALK INTERSECTIONS [J].

BURDZY, K ;

LAWLER, GF ;

POLASKI, T .

JOURNAL OF STATISTICAL PHYSICS, 1989, 56 (1-2) :1-12

[3]

BURDZY K, IN PRESS ANN PROBAB

[4]

Csorgo M., 1981, STRONG APPROXIMATION

[5]

Doob J., 1984, GRUNDLEHREN MATH WIS

[6] CONFORMAL-INVARIANCE AND INTERSECTIONS OF RANDOM-WALKS [J].

DUPLANTIER, B ;

KWON, KH .

PHYSICAL REVIEW LETTERS, 1988, 61 (22) :2514-2517

[7]

DVORETZKY A., 1950, ACTA SCI MATH SZEGED, V12, P75

[8]

Erdos P., 1960, ACTA MATH ACAD SCI H, V11, P231, DOI [10.1007/BF02020942, DOI 10.1007/BF02020942]

[9]

LAWLER G, IN PRESS P LOND MATH

[10] INTERSECTIONS OF RANDOM-WALKS WITH RANDOM SETS [J].

LAWLER, GF .

ISRAEL JOURNAL OF MATHEMATICS, 1989, 65 (02) :113-132

← 1 2 →