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Approximation via Correlation Decay when Strong Spatial Mixing Fails [article]

Ivona Bezakova, Andreas Galanis, Leslie Ann Goldberg, Heng Guo, Daniel Stefankovic
2019 arXiv   pre-print
Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing (SSM).  ...  This enables us to show correlation decay and to obtain an FPTAS even when SSM fails.  ...  This enables us to show correlation decay and to obtain an FPTAS even when strong spatial mixing fails.  ... 
arXiv:1510.09193v5 fatcat:6sfo5wbw35be7cuufomydxclla

Approximation via Correlation Decay When Strong Spatial Mixing Fails

Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, Heng Guo, Daniel Štefankovič
2019 SIAM journal on computing (Print)  
This enables us to show correlation decay and to obtain an FPTAS even when strong spatial mixing fails.  ...  Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing.  ...  This enables us to show correlation decay and to obtain an FPTAS even when strong spatial mixing fails.  ... 
doi:10.1137/16m1083906 fatcat:b3atsdayz5a5fadr6t4ghyilci

Approximation via Correlation Decay When Strong Spatial Mixing Fails * † ‡ §

Ivona Bezáková, Andreas Galanis, Leslie Goldberg, Heng Guo, Daniel Štefankovič
unpublished
This enables us to show correlation decay and to obtain an FPTAS even when strong spatial mixing fails.  ...  Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing.  ...  This enables us to show correlation decay and to obtain an FPTAS even when strong spatial mixing fails.  ... 
fatcat:bzx7hfptvfbrhiug7qjav4wjme

On Local Distributed Sampling and Counting [article]

Weiming Feng, Yitong Yin
2018 arXiv   pre-print
spatial mixing.  ...  Combining with the state of the arts of strong spatial mixing, we obtain efficient sampling algorithms in the LOCAL model for various important sampling problems, including: an O(√(Δ)^3n)-round algorithm  ...  An important decay of correlation property for joint distributions is the strong spatial mixing. We adopt the definition of strong spatial mixing in [21] into our context.  ... 
arXiv:1802.06686v1 fatcat:xdakhslhdnh3veu5wkexjwqek4

Exchange-correlation asymptotics and high harmonic spectra

Michael R. Mack, Daniel Whitenack, Adam Wasserman
2013 Chemical Physics Letters  
In other words, one might not expect the A-LDA spectrum at this frequency to have strong mixing between these two highest energy orbitals because the frequency is not resonant with the approximate excitation  ...  For example, it fails to support a Rydberg series of bound states and poorly approximates the ionization potential of the system via Koopmans' theorem [20] [21] [22] ; these are manifestations of self-interaction  ... 
doi:10.1016/j.cplett.2012.11.045 fatcat:pmqlhsd5t5gmtc7m3xw4lbchuq

Correlation Decay up to Uniqueness in Spin Systems [article]

Liang Li, Pinyan Lu, Yitong Yin
2021 arXiv   pre-print
We give a complete characterization of the two-state anti-ferromagnetic spin systems which are of strong spatial mixing on general graphs.  ...  We show that a two-state anti-ferromagnetic spin system is of strong spatial mixing on all graphs of maximum degree at most Δ if and only if the system has a unique Gibbs measure on infinite regular trees  ...  Two questions remain open for our complete understanding of the correlation decay and computation in two-state spin systems: the characterizations of the strong spatial mixing and approximability of general  ... 
arXiv:1111.7064v3 fatcat:4ufpoyr6ybagncgrgcjom4tq2i

Correlation decay and partition function zeros: Algorithms and phase transitions [article]

Jingcheng Liu and Alistair Sinclair and Piyush Srivastava
2022 arXiv   pre-print
We show further that our methods extend to the case when weak spatial mixing on the Bethe lattice is not known to be equivalent to strong spatial mixing on all graphs.  ...  We explore connections between the phenomenon of correlation decay and the location of Lee-Yang and Fisher zeros for various spin systems.  ...  JL was a PhD student at UC Berkeley when this work was carried out. JL and AS were supported by US NSF grant CCF-1815328.  ... 
arXiv:1906.01228v6 fatcat:6qeo7cwcangt7n2dto6rhxp2c4

Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model [article]

Nima Anari, Kuikui Liu, Shayan Oveis Gharan
2020 arXiv   pre-print
This improves the quasi-polynomial running time of Weitz's deterministic correlation decay algorithm for estimating the hardcore partition function, also answering a long-standing open problem of mixing  ...  Using a line of recent works on mixing time of high dimensional walks on simplicial complexes , this implies that the corresponding Glauber dynamics mixes rapidly and generates (approximate) samples from  ...  Theorem 2.13 (Weak Spatial Mixing Implies Strong Spatial Mixing; [Wei06] ). Assume λ = (1 − δ)λ c (∆) for some 0 < δ < 1.  ... 
arXiv:2001.00303v3 fatcat:g4gzn2kobbgkhmbnff7qhgvawm

Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems [article]

Heng Guo, Pinyan Lu
2018 arXiv   pre-print
Our technique is based on the correlation decay framework. The main technical contribution is a new potential function, with which we establish a new kind of spatial mixing.  ...  We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes.  ...  In particular, when β > 1 strong spatial mixing fails for any λ even if λ < λ c .  ... 
arXiv:1511.00493v3 fatcat:zpaumhkfsjb3pfmz2e7er3adcy

Spatial dynamics of invasion: the geometry of introduced species

Gyorgy Korniss, Thomas Caraco
2005 Journal of Theoretical Biology  
To analyze this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions.  ...  Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process.  ...  Toroczkai for helping us implementing a numerical integrator routine for the mean-field and pair approximations. G. K. is supported in part by NSF through Grant No.  ... 
doi:10.1016/j.jtbi.2004.09.018 pmid:15615627 fatcat:vnhhmhoqnbegfpw3iawrp3mkaq

Breaking the entanglement barrier: Tensor network simulation of quantum transport [article]

Marek M. Rams, Michael Zwolak
2019 arXiv   pre-print
interface, they scatter, generating a "bit" of entanglement between spatial regions with each event.  ...  large classes of quantum many-body systems have limited -- or efficiently representable -- entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via  ...  The mixed-basis, though, enables the simulation to go out to a time extensive in the reservoir size. When D is too small, it will lose accuracy, but it does not abruptly fail.  ... 
arXiv:1904.12793v1 fatcat:chqgmcvqerajtl4wglwd6z2rxi

Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure

Da-Jiang Liu, James W. Evans
2015 Journal of Chemical Physics  
of the spatial correlations in that state.  ...  Despite the lack of adspecies interactions, negligible adspecies diffusion results in kinetically induced spatial correlations.  ...  If such correlations are not too strong, they can be effectively characterized via Ursell-Mayer cluster expansions, or Kirkwood or quasi-chemical approximations. 4, 5 These correlations also satisfy  ... 
doi:10.1063/1.4916380 pmid:25854254 fatcat:6l7u2eyfgvgezk6ivaur4z5iry

Liquid pair correlations in four spatial dimensions: theory versus simulation

Marco Heinen, Jürgen Horbach, Hartmut Löwen
2015 Molecular Physics  
Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions.  ...  [43] , the latter approximation is exact in the limit of infinite spatial dimension (d → ∞), and remains to be a good approximation of the actual particle pair correlations for dimensions d 100.  ...  becomes very strong.  ... 
doi:10.1080/00268976.2014.993736 fatcat:qvzizpd7gbacraenbzp5dy7spu

Approximation algorithms for the random-field Ising model [article]

Tyler Helmuth, Holden Lee, Will Perkins, Mohan Ravichandran, Qiang Wu
2021 arXiv   pre-print
that no polynomial-time approximation scheme exists.  ...  These regions, which may have connected components of size Θ(log n), are a barrier to algorithms based on establishing a zero-free region, and cause worst-case analyses of Glauber dynamics to fail.  ...  We will that show strong spatial mixing, a strong form of correlation decay, holds with high probability on a tree when the typical value of |h x | is large enough.  ... 
arXiv:2108.11889v1 fatcat:dlnsqyly7bacnlq37qizklbxou

Evaluating model misspecification in independent component analysis

Seonjoo Lee, Brian S. Caffo, Balaji Lakshmanan, Dzung L. Pham
2013 Journal of Statistical Computation and Simulation  
Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters.  ...  In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases.  ...  as "decaying echoic mixing".  ... 
doi:10.1080/00949655.2013.867961 pmid:25642002 pmcid:PMC4309392 fatcat:ezikpovjefbppojmldxoqpej54
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