### Abstract

By means of random matrix approximation procedure, we re-prove Biane and Voiculescu's free analog of Talagrand's transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.

Original language | English |
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Pages (from-to) | 199-221 |

Number of pages | 23 |

Journal | Probability Theory and Related Fields |

Volume | 130 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Probability Theory and Related Fields*,

*130*(2), 199-221. https://doi.org/10.1007/s00440-004-0351-1

**Free transportation cost inequalities via random matrix approximation.** / Hiai, Fumio; Petz, Dénes; Ueda, Yoshimichi.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 130, no. 2, pp. 199-221. https://doi.org/10.1007/s00440-004-0351-1

}

TY - JOUR

T1 - Free transportation cost inequalities via random matrix approximation

AU - Hiai, Fumio

AU - Petz, Dénes

AU - Ueda, Yoshimichi

PY - 2004/10/1

Y1 - 2004/10/1

N2 - By means of random matrix approximation procedure, we re-prove Biane and Voiculescu's free analog of Talagrand's transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.

AB - By means of random matrix approximation procedure, we re-prove Biane and Voiculescu's free analog of Talagrand's transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.

UR - http://www.scopus.com/inward/record.url?scp=5644231165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5644231165&partnerID=8YFLogxK

U2 - 10.1007/s00440-004-0351-1

DO - 10.1007/s00440-004-0351-1

M3 - Article

VL - 130

SP - 199

EP - 221

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 2

ER -