ON THE STATISTICAL-MECHANICS APPROACH IN THE RANDOM-MATRIX THEORY - INTEGRATED DENSITY-OF-STATES

被引：93
|
作者：
DEMONVEL, AB [1 ]
PASTUR, L [1 ]
SHCHERBINA, M [1 ]
机构：
[1] KHARKOV LOW TEMP PHYS & ENGN INST,DIV MATH,KHARKOV 310164,UKRAINE
来源：
JOURNAL OF STATISTICAL PHYSICS | 1995年 / 79卷 / 3-4期
关键词：
RANDOM MATRIX; INTEGRATING DENSITY OF STATES; STATISTICAL MECHANICS; MEAN FIELD-THEORY;
D O I：
10.1007/BF02184872
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the ensemble of random symmetric n x n matrices specified by an orthogonal invariant probability distribution. We treat this distribution as a Gibbs measure of a mean-field-type model. This allows us to show that the normalized eigenvalue counting function of this ensemble converges in probability to a nonrandom limit as n --> infinity and that this limiting distribution is the solution of a certain self-consistent equation.
引用
收藏
页码：585 / 611
页数：27
相关论文
共 50 条
  • [11] STATISTICAL-MECHANICS OF RANDOM BICONTINUOUS PHASES
    PIERUSCHKA, P
    MARCELJA, S
    JOURNAL DE PHYSIQUE II, 1992, 2 (02): : 235 - 247
  • [12] HOMOGENEOUS RANDOM FIELDS AND STATISTICAL-MECHANICS
    ALBEVERIO, S
    HOEGHKROHN, R
    JOURNAL OF FUNCTIONAL ANALYSIS, 1975, 19 (03) : 242 - 272
  • [13] STATISTICAL-MECHANICS OF STATIONARY STATES .1. FORMAL THEORY
    PROCACCIA, I
    RONIS, D
    COLLINS, MA
    ROSS, J
    OPPENHEIM, I
    PHYSICAL REVIEW A, 1979, 19 (03): : 1290 - 1306
  • [14] RANDOM FIELD METHOD IN STATISTICAL-MECHANICS
    KUBAREV, SI
    THEORETICAL AND MATHEMATICAL PHYSICS, 1975, 22 (01) : 50 - 58
  • [15] ON THE RANDOM QFT FOUNDATIONS OF STATISTICAL-MECHANICS
    SYROS, C
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 1991, 5 (18): : 2909 - 2934
  • [16] STATISTICAL-MECHANICS OF RANDOM COIL NETWORKS
    GRAESSLEY, WW
    MACROMOLECULES, 1975, 8 (02) : 186 - 190
  • [17] Quantum graphs and random-matrix theory
    Pluhar, Z.
    Weidenmueller, H. A.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2015, 48 (27)
  • [18] NONEQUILIBRIUM STATISTICAL-MECHANICS APPROACH TO REACTION-RATE THEORY
    GRIGOLINI, P
    CHEMICAL PHYSICS, 1977, 21 (02) : 161 - 172
  • [19] EQUILIBRIUM STATES IN QUANTUM STATISTICAL-MECHANICS
    TORRES, PL
    ACTA CIENTIFICA VENEZOLANA, 1978, 29 : 76 - 76
  • [20] A random-matrix theory of the number sense
    Hannagan, T.
    Nieder, A.
    Viswanathan, P.
    Dehaene, S.
    PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2018, 373 (1740)
12345