Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 13 (2008) > Paper 40 open journal systems 


On Asymptotic Growth of the Support of Free Multiplicative Convolutions

Vladislav Kargin, Courant Institute of Mathematical Sciences


Abstract
Let μ be a compactly supported probability measure on the positive half-line with expectation 1 and variance V. Let μn denote the n-time free multiplicative convolution of μ with itself. Then, for large n the length of the support of μn is asymptotically equivalent to eVn, where e is the base of natural logarithms, e=2.71...


Full text: PDF | PostScript

Pages: 415-421

Published on: July 9, 2008


Bibliography
  1. Belinschi S. T. and H. Bercovici. Partially defined semigroups relative to multiplicative free convolution. Int Math. Res. Not. 2005 (2005), 65-101. Math. Review 2006f:46061
  2. Hiai F. and D. Petz The Semicircle Law, Free Random Variables And Entropy (2000) Am. Math. Society. Math. Review 2001j:46099
  3. Kargin V. The norm of products of free random variables. Prob. Th. and Rel. Fields 139 (2007), 397-413. Math. Review 2008g:46117
  4. Nica A. and R. Speicher Lectures on the Combinatorics of Free Probability (2006) Cambridge University Press. Math. Review 2266879
  5. Voiculescu D. Multiplication of Certain Non-commuting Random Variables. J. of Operator Theory 18 (1987), 223-235. Math. Review 89b:46076
  6. Voiculescu D., Dykema K. and A. Nica Free Random Variables (1992) Am. Math. Society. Math. Review 94c:46133
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X