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On constrained annealed bounds for pinning and wetting models
- Source :
- Electron. Commun. Probab. 10 (2005), 179-189, Scopus-Elsevier, Electronic Communications in Probability, Electronic Communications in Probability, 2005, 10 n.18, pp.179-189, Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2005, 10 n.18, pp.179-189
- Publication Year :
- 2005
- Publisher :
- arXiv, 2005.
-
Abstract
- The free energy of quenched disordered systems is bounded above by the free energy of the corresponding annealed system. This bound may be improved by applying the annealing procedure, which is just Jensen inequality, after having modified the Hamiltonian in a way that the quenched expressions are left unchanged. This procedure is often viewed as a partial annealing or as a constrained annealing, in the sense that the term that is added may be interpreted as a Lagrange multiplier on the disorder variables. In this note we point out that, for a family of models, some of which have attracted much attention, the multipliers of the form of empirical averages of local functions cannot improve on the basic annealed bound from the viewpoint of characterizing the phase diagram. This class of multipliers is the one that is suitable for computations and it is often believed that in this class one can approximate arbitrarily well the quenched free energy.<br />Comment: 10 pages
- Subjects :
- Statistics and Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Annealing (metallurgy)
82B44
Computation
Disordered Systems, Quenched Disorder, Annealed Models, Polymer Models, Effective Interface Models, Wetting Models
MathematicsofComputing_GENERAL
82B41
01 natural sciences
Combinatorics
InformationSystems_GENERAL
010104 statistics & probability
symbols.namesake
0103 physical sciences
FOS: Mathematics
Statistical physics
0101 mathematics
010306 general physics
GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries)
ComputingMilieux_MISCELLANEOUS
Mathematics
Phase diagram
Hardware_MEMORYSTRUCTURES
Probability (math.PR)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
60K35
Lagrange multiplier
symbols
Wetting
Statistics, Probability and Uncertainty
Hamiltonian (quantum mechanics)
Jensen's inequality
Mathematics - Probability
Subjects
Details
- ISSN :
- 1083589X
- Database :
- OpenAIRE
- Journal :
- Electron. Commun. Probab. 10 (2005), 179-189, Scopus-Elsevier, Electronic Communications in Probability, Electronic Communications in Probability, 2005, 10 n.18, pp.179-189, Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2005, 10 n.18, pp.179-189
- Accession number :
- edsair.doi.dedup.....e5338d5e8a64f8c4e9398332d98d1201
- Full Text :
- https://doi.org/10.48550/arxiv.math/0511562