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pro vyhledávání: '"Patras, Frédéric"'
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory has been developed primarily for specific applications in free probabi
Externí odkaz:
http://arxiv.org/abs/2407.17660
Autor:
Foissy, Loïc, Patras, Frédéric
We here construct an explicit isomorphism between any commutative Hopf algebra which underlying coalgebra is the tensor coalgebra of a space $V$ and the shuffle algebra based on the same space. This isomorphism uses the commutative $B_\infty$ structu
Externí odkaz:
http://arxiv.org/abs/2401.13317
Motivated by various developments in algebraic combinatorics and its applications, we investigate here the fine structure of a fundamental but little known theorem, the Gerstenhaber and Schack cohomology comparison theorem.The theorem classically ass
Externí odkaz:
http://arxiv.org/abs/2310.10288
Publikováno v:
Markov Processes and Related Fields 30, Issue 1, 2024, 149-178
Recent works have explored relations between classical and quantum statistical physics on the one hand and Voiculescu's theory of free probability on the other. Motivated by these results, the present work focuses on the notion of effective action, w
Externí odkaz:
http://arxiv.org/abs/2305.08871
Autor:
Chetrite, Raphael, Patras, Frederic
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture introduci
Externí odkaz:
http://arxiv.org/abs/2210.09264
Publikováno v:
Infinite Dimensional Analysis, Quantum Probability and Related Topics 27, No. 03, 2450005 (2024)
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie calculus,
Externí odkaz:
http://arxiv.org/abs/2208.02585
Publikováno v:
SIGMA 19 (2023), 038, 17 pages
We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra. This group law is left-linear and is therefore associated to a pre-Lie
Externí odkaz:
http://arxiv.org/abs/2204.01445
Autor:
Celestino, Adrian, Patras, Frédéric
Forest formulas that generalize Zimmermann's forest formula in quantum field theory have been obtained for the computation of the antipode in the dual of enveloping algebras of pre-Lie algebras. In this work, largely motivated by Murua's analysis of
Externí odkaz:
http://arxiv.org/abs/2203.11968
This chapter is divided into two parts. The first is largely expository and builds on Karandikar's axiomatisation of It{\^o} calculus for matrix-valued semimartin-gales. Its aim is to unfold in detail the algebraic structures implied for iterated It{
Externí odkaz:
http://arxiv.org/abs/2004.06945
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