SELF-AVOIDING WALK ON A HIERARCHICAL LATTICE IN 4 DIMENSIONS

被引：35
作者：
BRYDGES, D
EVANS, SN
IMBRIE, JZ
机构：
[1] UNIV CALIF BERKELEY,DEPT STAT,BERKELEY,CA 94720
[2] HARVARD UNIV,DEPT MATH,CAMBRIDGE,MA 02138
[3] HARVARD UNIV,DEPT PHYS,CAMBRIDGE,MA 02138
来源：
ANNALS OF PROBABILITY | 1992年 / 20卷 / 01期
关键词：
SELF-AVOIDING WALK; SUPERSYMMETRY; GRASSMAN INTEGRAL; RENORMALIZATION GROUP;
D O I：
10.1214/aop/1176989919
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：
We define a Levy process on a d-dimensional hierarchical lattice. By construction the Green's function for this process decays as \x\2-d . For d = 4, we prove that the introduction of a sufficiently weak self-avoidance interaction does not change this decay provided the mass = "killing" rate is chosen in a special way, so that the process is critical.
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页码：82 / 124
页数：43
相关论文
共 31 条
[1]   SOME PROBABILISTIC TECHNIQUES IN FIELD-THEORY [J].
BENFATTO, G ;
CASSANDRO, M ;
GALLAVOTTI, G ;
NICOLO, F ;
OLIVIERI, E ;
PRESUTTI, E ;
SCACCIATELLI, E .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 59 (02) :143-166
[2]  
BEREZIN FA, 1966, METHOD 2ND QUANTIZAT
[3]   INVESTIGATION OF CRITICAL-POINT IN MODELS OF TYPE OF DYSONS HIERARCHICAL MODELS [J].
BLEHER, PM ;
SINAI, JG .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1973, 33 (01) :23-42
[4]  
Brezin E., 1976, PHASE TRANSITIONS CR, V6
[5]   GRAD PHI-PERTURBATIONS OF MASSLESS GAUSSIAN FIELDS [J].
BRYDGES, D ;
YAU, HT .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 129 (02) :351-392
[6]  
BRYDGES D, 1983, COMMUN MATH PHYS, V83, P123
[7]  
Brydges D.C., 1991, J THEOR PROBAB, V4, P371
[8]   THE RANDOM-WALK REPRESENTATION OF CLASSICAL SPIN SYSTEMS AND CORRELATION INEQUALITIES .2. THE SKELETON INEQUALITIES [J].
BRYDGES, DC ;
FROHLICH, J ;
SOKAL, AD .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 91 (01) :117-139
[9]   A SUPERSYMMETRIC TRANSFER-MATRIX AND DIFFERENTIABILITY OF THE DENSITY OF STATES IN THE ONE-DIMENSIONAL ANDERSON MODEL [J].
CAMPANINO, M ;
KLEIN, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 104 (02) :227-241
[10]   EXPONENTS FOR EXCLUDED VOLUME PROBLEM AS DERIVED BY WILSON METHOD [J].
DEGENNES, PG .
PHYSICS LETTERS A, 1972, A 38 (05) :339-&
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