Results 91 to 100 of about 13,504 (178)
Cumulant Correlators in 2D and 3D Scale Free Simulations
, 1998 Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions and related moments.
Munshi, Dipak, Melott, Adrian L.
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Structured random matrices and cyclic cumulants: A free probability approach
Random Matrices: Theory and ApplicationsIn this paper, we introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise nonlinear operations. We then formulate an efficient method, based on an extremization problem, for computing the spectrum of subblocks of such ...
Bernard, Denis, Hruza, Ludwig
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Free cumulants of some probability measures [PDF]
Banach Center Publications, 2007 Melanie Hinz, Wojciech Młotkowski
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Asymptotic limit of cumulants and higher order free cumulants of complex Wigner matrices
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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Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling
Out-of-time-order correlation functions (OTOCs) and their higher-order generalizations present important probes of quantum information dynamics and scrambling. We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable.
Fritzsch, Felix +3 more
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Second order free cumulants: product, commutator, and anti-commutator
Given two second order free random variables $a$ and $b$, we study the second order free cumulants of their product $ab$, their commutator $ab-ba$, and their anti-commutator $ab+ba$. Let $(κ_n^a)_{n\geq 1}$ and $(κ_{n,m}^a)_{n,m\geq 1}$ denote the sequence of free cumulants of first and second order, respectively, of a random variable $a$ in a second ...
George, Daniel Munoz, Perales, Daniel
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Scaling of free cumulants in closed system-bath setups
The 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 ETH and postulates a smooth function to describe the multi-point correlations among matrix elements.
Füllgraf, Merlin +2 more
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Critical points of random polynomials and finite free cumulants
13 pages.
Arizmendi, Octavio +2 more
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A Note on Cumulant Technique in Random Matrix Theory. [PDF]
Entropy (Basel), 2023 Soshnikov A, Wu C.
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Correlations in Uniform Spanning Trees: a Fermionic Approach. [PDF]
J Stat PhysRapoport A.
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