Equidistribution of Equidistant Level Sets to Gibbs Measures

2019 ◽  
pp. 207-224
Author(s):  
Anne Broise-Alamichel ◽  
Jouni Parkkonen ◽  
Frédéric Paulin
Keyword(s):  
Level Sets ◽  
Gibbs Measures

Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages

2009 ◽  
Vol 29 (3) ◽  
pp. 885-918 ◽  
Author(s):  
DE-JUN FENG ◽  
LIN SHU
Keyword(s):  
Convex Analysis ◽  
Level Sets ◽  
Multifractal Analysis ◽  
Gibbs Measures ◽  
Thermodynamic Formalism

AbstractThe paper is devoted to the study of the multifractal structure of disintegrations of Gibbs measures and conditional (random) Birkhoff averages. Our approach is based on the relativized thermodynamic formalism, convex analysis and, especially, the delicate constructions of Moran-like subsets of level sets.

Translation-Invariant Gibbs Measures for the Blum-Kapel Model on a Cayley Tree

2016 ◽  
Vol 15 (2) ◽  
pp. 239-255 ◽  
Author(s):  
Nosir Khatamov ◽  
◽  
Rustam Khakimov ◽  
Keyword(s):  
Cayley Tree ◽  
Gibbs Measures ◽  
Translation Invariant

Perfect level sets in many directions

1986 ◽  
Vol 12 (1) ◽  
pp. 176
Author(s):  
Malý
Keyword(s):  
Level Sets

LEVEL SETS OF A TYPICAL C n FUNCTION

1998 ◽  
Vol 24 (1) ◽  
pp. 83
Author(s):  
Darji ◽  
Morayne
Keyword(s):  
Level Sets

scholarly journals On Gibbs Measures and Spectra of Ruelle Transfer Operators

2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Frobenius Theorem ◽  
Transfer Operators

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

scholarly journals PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

2008 ◽  
Vol 20 (05) ◽  
pp. 529-595 ◽  
Author(s):  
ALINA KARGOL ◽  
YURI KONDRATIEV ◽  
YURI KOZITSKY
Keyword(s):  
Phase Transitions ◽  
Gibbs Measures ◽  
Quantum Effects ◽  
Gibbs States ◽  
Translation Invariance ◽  
Unified Theory ◽  
The Relationship ◽  
Anharmonic Crystals

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

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