Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems
We consider reversible, conservative Ginzburg–Landau processes, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. Following the martingale approach introduced in (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for K...
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| Veröffentlicht in: | Annales de l'I.H.P. Probabilités et statistiques 2002, Vol.38 (5), p.739-777 |
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| creator | Landim, C. Panizo, G. Yau, H.T. |
| description | We consider reversible, conservative Ginzburg–Landau processes, whose potential are bounded perturbations of the Gaussian potential, evolving on a
d-dimensional cube of length
L. Following the martingale approach introduced in (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), we prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order
L
−2.
Nous considérons des processus de Ginzburg–Landau réversibles, dont le potentiel est une perturbation bornée du potential Gaussien, évoluent sur un cube
d-dimensionel de largeur
L. Suivant la méthode martingale introduite dans (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), nous démontrons qu'en toute dimension le trou spectral et la constante de Sobolev logarithmique sont d'ordre
L
−2. |
| doi_str_mv | 10.1016/S0246-0203(02)01108-1 |
| format | Article |
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d-dimensional cube of length
L. Following the martingale approach introduced in (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), we prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order
L
−2.
Nous considérons des processus de Ginzburg–Landau réversibles, dont le potentiel est une perturbation bornée du potential Gaussien, évoluent sur un cube
d-dimensionel de largeur
L. Suivant la méthode martingale introduite dans (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), nous démontrons qu'en toute dimension le trou spectral et la constante de Sobolev logarithmique sont d'ordre
L
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d-dimensional cube of length
L. Following the martingale approach introduced in (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), we prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order
L
−2.
Nous considérons des processus de Ginzburg–Landau réversibles, dont le potentiel est une perturbation bornée du potential Gaussien, évoluent sur un cube
d-dimensionel de largeur
L. Suivant la méthode martingale introduite dans (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), nous démontrons qu'en toute dimension le trou spectral et la constante de Sobolev logarithmique sont d'ordre
L
−2.</description><subject>Exact sciences and technology</subject><subject>Interacting particle systems</subject><subject>Limit theorems</subject><subject>Logarithmic Sobolev inequality</subject><subject>Mathematics</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Sciences and techniques of general use</subject><subject>Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)</subject><subject>Spectral gap</subject><issn>0246-0203</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNo90E1LAzEQBuAcFKwfP0HIRdDD6mS3m25OIsUvKHio4jHMJpMa2WbXZLvQf--2FS8zMLy8DA9jlwJuBQh5t4R8KjPIobiG_AaEgCoTR2zyfz5hpyl9A4BUICfsc9mR6SM2fIUdx2B5064w-v5r7Q1ftnXb0MB9oJ8NNr7fctdGvgl1uwmWLDdtSBQH7P1APHU-8LRNPa3TOTt22CS6-Ntn7OPp8X3-ki3enl_nD4uM8kL1GRpJBFQYiwYdyrLKK6iso5mSqpLSGeVmpXGitiCmlbIWa1k5a3OlQElbnLGrQ2-HyWDjIgbjk-6iX2PcalFUpchLMebuDzkanxk8RZ2Mp2DI-jgCaNt6LUDvDPXeUO-wxqH3hmPRL7yOaeU</recordid><startdate>2002</startdate><enddate>2002</enddate><creator>Landim, C.</creator><creator>Panizo, G.</creator><creator>Yau, H.T.</creator><general>Elsevier Masson SAS</general><general>Elsevier</general><scope>IQODW</scope></search><sort><creationdate>2002</creationdate><title>Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems</title><author>Landim, C. ; Panizo, G. ; Yau, H.T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-e239t-ac6ee0e3cdacafa6582808dfe7969866fc9f75cf1bd01489ddab68fdd299096d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Exact sciences and technology</topic><topic>Interacting particle systems</topic><topic>Limit theorems</topic><topic>Logarithmic Sobolev inequality</topic><topic>Mathematics</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Sciences and techniques of general use</topic><topic>Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)</topic><topic>Spectral gap</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Landim, C.</creatorcontrib><creatorcontrib>Panizo, G.</creatorcontrib><creatorcontrib>Yau, H.T.</creatorcontrib><collection>Pascal-Francis</collection><jtitle>Annales de l'I.H.P. Probabilités et statistiques</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Landim, C.</au><au>Panizo, G.</au><au>Yau, H.T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems</atitle><jtitle>Annales de l'I.H.P. Probabilités et statistiques</jtitle><date>2002</date><risdate>2002</risdate><volume>38</volume><issue>5</issue><spage>739</spage><epage>777</epage><pages>739-777</pages><issn>0246-0203</issn><coden>AHPBAR</coden><abstract>We consider reversible, conservative Ginzburg–Landau processes, whose potential are bounded perturbations of the Gaussian potential, evolving on a
d-dimensional cube of length
L. Following the martingale approach introduced in (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), we prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order
L
−2.
Nous considérons des processus de Ginzburg–Landau réversibles, dont le potentiel est une perturbation bornée du potential Gaussien, évoluent sur un cube
d-dimensionel de largeur
L. Suivant la méthode martingale introduite dans (S.L. Lu, H.T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 433–499), nous démontrons qu'en toute dimension le trou spectral et la constante de Sobolev logarithmique sont d'ordre
L
−2.</abstract><cop>Paris</cop><pub>Elsevier Masson SAS</pub><doi>10.1016/S0246-0203(02)01108-1</doi><tpages>39</tpages></addata></record> |
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| ispartof | Annales de l'I.H.P. Probabilités et statistiques, 2002, Vol.38 (5), p.739-777 |
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| subjects | Exact sciences and technology Interacting particle systems Limit theorems Logarithmic Sobolev inequality Mathematics Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Spectral gap |
| title | Spectral gap and logarithmic Sobolev inequality for unbounded conservative spin systems |
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