A log-Sobolev type inequality for free entropy of two projections
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 1, pp. 239-249.

Nous prouvons un genre d'inégalité de Sobolev logarithmique qui montre que l'information de Fisher libre domine l'entropie de micro-états libre adaptée aux projections dans le cas de deux projections.

We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.

DOI : https://doi.org/10.1214/08-AIHP164
Classification : 46L54,  94A17,  60E15
Mots clés : logarithmic Sobolev inequality, free entropy, mutual free Fisher information
@article{AIHPB_2009__45_1_239_0,
     author = {Hiai, Fumio and Ueda, Yoshimichi},
     title = {A log-Sobolev type inequality for free entropy of two projections},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {239--249},
     publisher = {Gauthier-Villars},
     volume = {45},
     number = {1},
     year = {2009},
     doi = {10.1214/08-AIHP164},
     zbl = {1178.46066},
     mrnumber = {2500237},
     language = {en},
     url = {http://www.numdam.org/articles/10.1214/08-AIHP164/}
}
Hiai, Fumio; Ueda, Yoshimichi. A log-Sobolev type inequality for free entropy of two projections. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 1, pp. 239-249. doi : 10.1214/08-AIHP164. http://www.numdam.org/articles/10.1214/08-AIHP164/

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