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

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.

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.

DOI : https://doi.org/10.1214/08-AIHP164
Classification:  46L54,  94A17,  60E15
Keywords: 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},
     publisher = {Gauthier-Villars},
     volume = {45},
     number = {1},
     year = {2009},
     pages = {239-249},
     doi = {10.1214/08-AIHP164},
     zbl = {1178.46066},
     mrnumber = {2500237},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2009__45_1_239_0}
}
Hiai, Fumio; Ueda, Yoshimichi. A log-Sobolev type inequality for free entropy of two projections. Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 1, pp. 239-249. doi : 10.1214/08-AIHP164. http://www.numdam.org/item/AIHPB_2009__45_1_239_0/

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