Effective Action in Free Probability

被引：0
作者：
Ebrahimi-Fard, Kurusch [1 ]
Patras, Frederic [2 ]
机构：
[1] NTNU, Dept Math Sci, NO-7491 Trondheim, Norway
[2] Univ Cote dAzur, CNRS, UMR 7351, Parc Valrose, F-06108 Nice 02, France
来源：
MARKOV PROCESSES AND RELATED FIELDS | 2024年 / 30卷 / 01期
关键词：
effective action; free probability; free cumulants; planar Feynman diagrams; one-particle irreducibility;
D O I：
10.61102/1024-2953-mprf.2024.30.1.006
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：
Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these results, the present work focuses on the notion of effective action, which is closely related to the large deviation rate function in classical probability and one -particle irreducible correlation functions in quantum field theories. The central aim is to understand how it can be defined and studied in free probability. In this respect, we introduce a suitable diagrammatic formalism.
引用
收藏
页数：181
相关论文
共 30 条
  • [1] [Anonymous], 1992, Free Random Variables
  • [2] Monotone Cumulant-Moment Formula and Schroder Trees
    Arizmendi, Octavio
    Celestino, Adrian
    [J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2022, 18
  • [3] Bernoulli Variables, Classical Exclusion Processes and Free Probability
    Bauer, Michel
    Bernard, Denis
    Biane, Philippe
    Hruza, Ludwig
    [J]. ANNALES HENRI POINCARE, 2024, 25 (01): : 125 - 172
  • [4] Exact entanglement in the driven quantum symmetric simple exclusion process
    Bernard, Denis
    Hruza, Ludwig
    [J]. SCIPOST PHYSICS, 2023, 15 (04):
  • [5] Biane P., 2002, P INT C MATHEMATICIA, P765
  • [6] Borot G, 2023, Arxiv, DOI [arXiv:2112.12184, 10.48550/arXiv.2112.12184, DOI 10.48550/ARXIV.2112.12184]
  • [7] PLANAR DIAGRAMS
    BREZIN, E
    ITZYKSON, C
    PARISI, G
    ZUBER, JB
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 59 (01) : 35 - 51
  • [8] BROUDER CH., 2011, Contemporary Mathematics, V539, P1
  • [9] CARTIER P., 2021, Classical Hopf Algebras and their Applications
  • [10] THE PLANAR SECTOR OF FIELD-THEORIES
    CVITANOVIC, P
    LAUWERS, PG
    SCHARBACH, PN
    [J]. NUCLEAR PHYSICS B, 1982, 203 (03) : 385 - 412
123