Random matrix ensembles: Wang-Landau algorithm for spectral densities

Kumar, Santosh

doi:10.1209/0295-5075/101/20002

Cited by 5 publications

(4 citation statements)

References 31 publications

(105 reference statements)

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“…If the desired observable does not depend only on the energy (as the spectrum of the triangulation), but on some other details of the state, one cannot apply Eq. (21) and has the following two options: First one can extend the simulation and perform a sampling of the extended density of states g(E, O) [48]. In many cases this is not applicable, such as in lattice triangulations, since the resulting phase space is more complicated and the sampling of the extended density of states needs too much computation time.…”

Section: Canonical Ensemblementioning

confidence: 99%

“…In many cases this is not applicable, such as in lattice triangulations, since the resulting phase space is more complicated and the sampling of the extended density of states needs too much computation time. The second option is to calculate first the density of states g(E) using the standard Wang-Landau algorithm and then to use the obtained estimation of g(E) to do a flat-histogram sampling with weights (20) and to record the combined (normalized) histogram H(E, A) which counts the occurrence of observable outcomes A at certain energies E [36,78,79,48]. The canonical expectation value of the observable can then be calculated using…”

Section: Canonical Ensemblementioning

confidence: 99%

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Spectral Properties of Unimodular Lattice Triangulations

2016

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Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance, Markov chain Monte-Carlo simulations can be applied to study these graphs. Here, we consider the spectra of the adjacency and the Laplacian matrix as well as the algebraic connectivity and the spectral radius. Power law dependencies on the system size can clearly be identified and compared to analytical solutions for periodic ground states. For random triangulations we find a qualitative agreement of the spectral properties with well-known random graph models. In the microcanonical ensemble analytical approximations agree with numerical simulations. In the canonical ensemble a crossover behaviour can be found for the algebraic connectivity and the spectral radius, thus combining large-world and small-world behavior in one model. The considered spectral properties can be applied to transport problems on triangulation graphs and the crossover behaviour allows a tuning of important transport quantities.

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Section: Canonical Ensemblementioning

confidence: 99%

Section: Canonical Ensemblementioning

confidence: 99%

Spectral Properties of Unimodular Lattice Triangulations

2016

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“…The results in this subsection are discussed in detail in Saito et al (2010) and Saito and Iba (2011). Kumar (2013) also applied the Wang-Landau algorithm to random matrices using coulomb gas formulation.…”

Section: Rare Events In Random Matricesmentioning

confidence: 99%

Multicanonical MCMC for sampling rare events: an illustrative review

2014

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Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or Metropolis-coupled MCMC) is also explained as an alternative to multicanonical MCMC. In the last section, multicanonical MCMC is applied to data surrogation; a successful implementation in surrogating time series is shown. In the appendices, calculation of averages and normalizing constant in an exponential family, phase coexistence, simulated tempering, parallelization, and multivariate extensions are discussed.

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“…Owing to several refinements and improvements , it has been gradually implemented to study complicated systems with continuous energy spectra as well. Examples include complex fluids [3][4][5], atomic clusters [6,7], liquid crystals [8], biomolecules [9][10][11], polymers [12][13][14][15], logarithmic gas in the context of random matrix theory [29], etc.…”

Section: Introductionmentioning

confidence: 99%

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

Kumar

Chandramouli

et al. 2018

Phys. Rev. E

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We consider a class of systems where N identical particles with positions q1, ..., qN and momenta p1, ..., pN are enclosed in a box of size L, and exhibit the scaling U(Lr1, ..., LrN ) = α(L) U(r1, ..., rN ) for the associated potential energy function U(q1, ..., qN ). For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description, and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach, as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box. arXiv:1810.11623v2 [cond-mat.stat-mech]

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Random matrix ensembles: Wang-Landau algorithm for spectral densities

Cited by 5 publications

References 31 publications

Spectral Properties of Unimodular Lattice Triangulations

Spectral Properties of Unimodular Lattice Triangulations

Multicanonical MCMC for sampling rare events: an illustrative review

Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

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