Displaying similar documents to “A free analogue of the transportation cost inequality on the circle”

Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

A log-Sobolev type inequality for free entropy of two projections

Fumio Hiai, Yoshimichi Ueda (2009)

Annales de l'I.H.P. Probabilités et statistiques

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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.

The square model for random groups

Tomasz Odrzygóźdź (2016)

Colloquium Mathematicae

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We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model...

On risk minimizing strategies for default-free bond portfolio immunization

Marek Kałuszka, Alina Kondratiuk-Janyska (2004)

Applicationes Mathematicae

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This paper presents new strategies for bond portfolio immunization which combine the time-honored duration with the M-Absolute measure defined by Nawalkha and Chambers (1996). The innovation consists in considering an average shock in a fixed time period as a random variable with mean μ or, alternatively, with normal distribution with mean μ and variance σ². Additionally, an extension to arbitrage free models of polynomial shocks is provided. Moreover, the Fisher and Weil model, the...