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Semigroups related to additive and multiplicative, free and Boolean convolutions

Octavio Arizmendi, Takahiro Hasebe (2013)

Studia Mathematica

Belinschi and Nica introduced a composition semigroup of maps on the set of probability measures. Using this semigroup, they introduced a free divisibility indicator, from which one can know quantitatively if a measure is freely infinitely divisible or not. In the first half of the paper, we further investigate this indicator: we calculate how the indicator changes with respect to free and Boolean powers; we prove that free and Boolean 1/2-stable laws have free divisibility indicators equal to infinity;...

Sharp uniform convexity and smoothness inequalities for trace norms.

E.H. Lieb, Keith Ball, E.A. Carlen (1994)

Inventiones mathematicae

Some comments on quantum probability

Kalyanapuram Rangachari Parthasarathy (1989)

Séminaire de probabilités de Strasbourg

Some remarks on the convergence in measure and on a dominated sequence of operators measurable with respect to a semifinite von Neumann algebra

Leszek Jan Ciach (1988)

Colloquium Mathematicae

Some results on non-commutative Banach function spaces.

Keiichi Watanabe (1992)

Mathematische Zeitschrift

Spectral distribution of the free Jacobi process associated with one projection

Nizar Demni, Taoufik Hmidi (2014)

Colloquium Mathematicae

Given an orthogonal projection P and a free unitary Brownian motion $Y = {(Y ₜ)}_{t \geq 0}$ in a W*-non commutative probability space such that Y and P are *-free in Voiculescu’s sense, we study the spectral distribution νₜ of Jₜ = PYₜPYₜ*P in the compressed space. To this end, we focus on the spectral distribution μₜ of the unitary operator SYₜSYₜ*, S = 2P - 1, whose moments are related to those of Jₜ via a binomial-type expansion already obtained by Demni et al. [Indiana Univ. Math. J. 61 (2012)]. In this connection,...

Stable laws and domains of attraction in free probability theory.

Bercovici, Hari, Pata, Vittorino (1999)

Annals of Mathematics. Second Series

Stationary Quantum Markov processes as solutions of stochastic differential equations

Jürgen Hellmich, Claus Köstler, Burkhard Kümmerer (1998)

Banach Center Publications

From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution. In this report we describe some recent work, showing that this general structure already allows a rich theory of stochastic integration and stochastic differential equations. In particular, if a quantum Markov process is represented by a unitary cocycle, we can...

Subadditive measures on projectors of a von Neumann algebra [Book]

Leszek J. Ciach (1990)

Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

Wojciech Młotkowski, Noriyoshi Sakuma (2011)

Banach Center Publications

We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then ${(μ ₁ ⨄ μ ₂)}^{s} = μ ₁^{s} ⨄ μ ₂^{s}$ and if ν₁,ν₂ are symmetric then ${(ν ₁ ⨄ ν ₂)}^{(2)} = ν ₁^{(2)} ⨄ ν ₂^{(2)}$ . Finally we investigate necessary and sufficient conditions under which the latter equality holds.

Displaying 1 – 10 of 10

Subadditive measures on projectors of a von Neumann algebra [Book]

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