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Complete Gradient Estimates of Quantum Markov Semigroups. [PDF]
Commun Math Phys, 2021 AbstractIn this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable
Wirth M, Zhang H.
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On the Feynman–Kac semigroup for some Markov processes [PDF]
Modern Stochastics: Theory and Applications, 2015 For a (non-symmetric) strong Markov process X, consider the Feynman–Kac semigroup \[{T_{t}^{A}}f(x):={\mathbb{E}}^{x}\big[{e}^{A_{t}}f(X_{t})\big],\hspace{1em}x\in {\mathbb{R}}^{n},\hspace{2.5pt}t>0,\] where A is a continuous additive functional of X ...
Victoria Knopova
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Markov semigroups, monoids, and groups [PDF]
International Journal of Algebra and Computation, 2012 A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper
Alan J. Cain +9 more
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Generators of quantum Markov semigroups [PDF]
Journal of Mathematical Physics, 2015 Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works
George Androulakis, Matthew Ziemke
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Derivations and KMS-Symmetric Quantum Markov Semigroups. [PDF]
Commun Math Phys, 2023 AbstractWe prove that the generator of the $$L^2$$ L 2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for ...
Vernooij M, Wirth M.
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Skew convolution semigroups and affine Markov processes [PDF]
, 2006 A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup ...
Dawson, D. A., Li, Zenghu
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Quantum Markov Semigroups (Product Systems and Subordination) [PDF]
International Journal of Mathematics, 2005 We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable representation. We show, too, that the dual product system of a Borel product system also carries a natural Borel structure.
Paul S. Muhly, Baruch Solel
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Markov semigroups with simplest interaction, I [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1971 Yōichirō Takahashi
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A Measure-on-Graph-Valued Diffusion: A Particle System with Collisions and Its Applications
Mathematics, 2022 A diffusion-taking value in probability-measures on a graph with vertex set V, ∑i∈Vxiδi is studied. The masses on each vertex satisfy the stochastic differential equation of the form dxi=∑j∈N(i)xixjdBij on the simplex, where {Bij} are independent ...
Shuhei Mano
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Balance Between Quantum Markov Semigroups [PDF]
Annales Henri Poincaré, 2018 The concept of balance between two state preserving quantum Markov semigroups on von Neumann algebras is introduced and studied as an extension of conditions appearing in the theory of quantum detailed balance. This is partly motivated by the theory of joinings. Balance is defined in terms of certain correlated states (couplings), with entangled states
Duvenhage, Rocco de Villiers +1 more
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