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Decomposition of free cumulants
, 2023 61 pages, 4 figures, revised version: several proofs have been improved and a number of clarifications and examples have been ...
Lenczewski, Romuald
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An operadic approach to operator-valued free cumulants [PDF]
Higher Structures, 2018 An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
Drummond-Cole, Gabriel C.
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, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Josuat-Vergès, Matthieu +3 more
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Generalized free cumulants for quantum chaotic systems
Journal of High Energy PhysicsThe eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators.
Siddharth Jindal, Pavan Hosur
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On Free Moments and Free Cumulants
, 2014 The concepts of free cumulants and free moments are indispensably related to the idea of freeness introduced by Voiculescu [Voiculescu, D., Proc. Conf., Buşteni/Rom., Lect. Notes Math. 1132(1985), pp. 556-588] and studied further within Free probability theory. Free probability theory is of great importance for both the developing mathematical theories
Pielaszkiewicz, Jolanta +2 more
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Microcanonical free cumulants in lattice systems
Physical Review BRecently, the full version of the Eigenstate Thermalization Hypothesis (ETH) has been systematized using Free Probability. In this paper, we present a detailed discussion of the Free Cumulants approach to many-body dynamics within the microcanonical ensemble.
Fritzsch, Felix +2 more
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Finite N Precursors of the Free Cumulants
Annales Henri Poincaré48 pages, 1 figure, v3: small ...
Sylvain Lacroix, Jean-Bernard Zuber
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A group-theoretical approach to conditionally free cumulants [PDF]
, 2020 In this work we extend the recently introduced group-theoretical approach to moment-cumulant relations in non-commutative probability theory to the notion of conditionally free cumulants. This approach is based on a particular combinatorial Hopf algebra which may be characterised as a non-cocommutative generalisation of the classical unshuffle Hopf ...
Ebrahimi-Fard, Kurusch +1 more
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Asymptotic limit of cumulants and higher order free cumulants of complex Wigner matrices [PDF]
We compute the fluctuation moments $α_{m_1,\dots,m_r}$ of a Complex Wigner Matrix $X_N$ given by the limit $\lim_{N\rightarrow\infty}N^{r-2}k_r(Tr(X_N^{m_1}),\dots,Tr(X_N^{m_r}))$. We prove the limit exists and characterize the leading order via planar graphs that result to be trees.
Mingo, James A., George, Daniel Munoz
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Scaling of free cumulants in closed system-bath setups
SciPost Physics CoreThe Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional
Merlin Füllgraf, Jochen Gemmer, Jiaozi Wang
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