Voiculescu’s Entropy and Potential Theory
Thomas Bloom[1]
- [1] Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3 Canada
Annales de la faculté des sciences de Toulouse Mathématiques (2011)
- Volume: 20, Issue: S2, page 57-69
- ISSN: 0240-2963
Access Full Article
topAbstract
topHow to cite
topBloom, Thomas. "Voiculescu’s Entropy and Potential Theory." Annales de la faculté des sciences de Toulouse Mathématiques 20.S2 (2011): 57-69. <http://eudml.org/doc/219679>.
@article{Bloom2011,
abstract = {We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.},
affiliation = {Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3 Canada},
author = {Bloom, Thomas},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {large deviation; entropy; Markov's property; weighted potential theory},
language = {eng},
month = {4},
number = {S2},
pages = {57-69},
publisher = {Université Paul Sabatier, Toulouse},
title = {Voiculescu’s Entropy and Potential Theory},
url = {http://eudml.org/doc/219679},
volume = {20},
year = {2011},
}
TY - JOUR
AU - Bloom, Thomas
TI - Voiculescu’s Entropy and Potential Theory
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/4//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - S2
SP - 57
EP - 69
AB - We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.
LA - eng
KW - large deviation; entropy; Markov's property; weighted potential theory
UR - http://eudml.org/doc/219679
ER -
References
top- Baran (M.).— Complex equilibrium measure and Bernstein type theorems for compact sets in , Proc Am. Math. Soc. 123. no. 2, p. 485-494 (1995). Zbl0813.32011MR1219719
- Berman (R.).— Large deviations and entropy for determinental point processes on complex manifolds, arxiv:0812.4224.
- Berman (R.).— Determinental point processes and fermions on complex manifolds: bulk universality arxiv:0811.3341.
- Bloom (T.) and Levenberg (N.).— Capacity convergence results and applications to a Bernstein-Markov inequality, Tr. Am. Math Soc. 351. no. 12, p. 4753-4767 (1999). Zbl0933.31007MR1695017
- Bloom (T.) and Levenberg (N.).— Asymptotics for Christoffel functions of Planar Measures, J. D’Anal Math. 106, p. 353-371 (2008). Zbl1158.28001MR2448990
- Bloom (T.) and Levenberg (N.).— Transfinite diameter notions in and integrals of Van-DerMonde determinants, arxiv:0712.2844. Zbl1196.31003
- Bloom (T.).— Weighted polynomials and weighted pluripotential theory, Tr. Am. Math Soc. 361 no. 4, p. 2163-2179 (2009). Zbl1166.32019MR2465832
- Bloom (T.).— “Large Deviations for VanDerMonde determinants" talk given at the Work-shop on Complex Hyperbolic Geometry and Related Topics (November 17-21, 2008) at the Fields Institute. http://www.fields.utoronto.ca/audio/08-09/hyperbolic/bloom/.
- Ben Arous (G.) and Guionnet (A.).— Large deviation for Wigner’s law and Voiculescu’s non-commutative entopy, Prob. Th. Related Fields 108 (1997), p. 517-542. Zbl0954.60029MR1465640
- Ben Arous (G.) and Zeitouni (O.).— Large deviations from the circular law, ESAIM: Probability and Statistics 2, 123-134 (1998). Zbl0916.60022MR1660943
- Borwein (P.) and Erdelyi (T.).— Polynomials and Polynomial Inequalities, Springer Graduate Texts in Mathematics 161, New York (1995). Zbl0840.26002MR1367960
- Dembo (A.) and Zeitouni (O.).— Large Deviation Techniques and Applications, 2nd edition, Springer, New York (1998). Zbl1177.60035MR1619036
- Deift (P.).— Othogonal Polynomials and Random Matrices: A Riemann-Hilbert approach, AMS Providence RI (1999). Zbl0997.47033MR1677884
- Ellis (R.S.).— Entropy, Large Deviations and Statistical Mechanics, Springer, New York/Berlin (1985). Zbl1102.60087MR793553
- Hiai (F.) and Petz (D.).— The Semicircle Law, Free Random Variables and Entropy, AMS Providence RI (2000). Zbl0955.46037MR1746976
- Klimek (M.).— Pluripotential Theory, Oxford University Press, Oxford (1991). Zbl0742.31001MR1150978
- Plesniak (W.).— Inegalite de Markov en plusieurs variables, Int. J of Math and Math. Science, Art ID 24549, p. 1-12 (2006). Zbl1153.41302MR2251749
- Saff (E.) and Totik (V.).— Logarithmic Potential with External Fields, Springer-Verlag, Berlin (1997). Zbl0881.31001MR1485778
- Stahl (H.) and Totik (V.).— General Orthogonal Polynomials, Cambridge Unviersity Press, Cambridge (1992). Zbl1187.33008MR1163828
- Voiculescu (D.).— The analogues of entropy and of Fisher’s information measure in free probability theory I, Comm. Math. Phy. 155, p. 71-92 (1993). Zbl0781.60006MR1228526
- Voiculescu (D.).— The analogues of entropy and of Fisher’s information measure in free probability II, Inv. Math. 118, p. 411-440 (1994). Zbl0820.60001MR1296352
- Zeitouni (O.) and Zelditch (S.).— Large Deviations of empirical zero point measures on Riemann surfaces, I : g = 0 arxiv:0904.4271.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.