Errors in measuring correlation functions of random processes with different probability distributions

1979 ◽  
Vol 22 (8) ◽  
pp. 913-917 ◽  
Author(s):  
G. Ya. Mirskii
Keyword(s):  
Correlation Functions ◽  
Probability Distributions ◽  
Random Processes

scholarly journals Six-vertex Models and the GUE-corners Process

2018 ◽  
Vol 2020 (6) ◽  
pp. 1794-1881
Author(s):  
Evgeni Dimitrov
Keyword(s):  
Correlation Functions ◽  
Probability Distributions ◽  
Gibbs Measures ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Difference Operators ◽  
Vertex Model ◽  
Gaussian Unitary Ensemble ◽  
Vertex Models ◽  
Higher Spin

Abstract We consider a class of probability distributions on the six-vertex model, which originates from the higher spin vertex models of [13]. We define operators, inspired by the Macdonald difference operators, which extract various correlation functions, measuring the probability of observing different arrow configurations. For the class of models we consider, the correlation functions can be expressed in terms of multiple contour integrals, which are suitable for asymptotic analysis. For a particular choice of parameters we analyze the limit of the correlation functions through the steepest descent method. Combining this asymptotic statement with some new results about Gibbs measures on Gelfand–Tsetlin cones and patterns, we show that the asymptotic behavior of our six-vertex model near the boundary is described by the Gaussian Unitary Ensemble-corners process.

scholarly journals Stochastic Hydrology: Is Scientific Understanding Growing?

2020 ◽  
Vol 163 ◽  
pp. 06001
Author(s):  
Mikhail Bolgov
Keyword(s):  
Climate Changes ◽  
Probability Distributions ◽  
Random Processes ◽  
Stochastic Hydrology ◽  
One Dimensional ◽  
Probabilistic Forecasts ◽  
Markovian Property ◽  
New Models ◽  
Complex Models ◽  
With Memory

Among many problems of stochastic hydrology, several major problems may be singled out. (1) The methodology problem – may fluctuation of hydro-meteorological values be considered within the framework of probabilities and random processes? Was this topic discussed after 1953? (2) One-dimensional probability distributions – is there progress? Are there new models? (3) Random Processes: Is Markovian property sufficient or more complex models with memory are needed? (4) Lack of stability resulting from climate changes: Is there progress in understanding the approaches to probabilistic forecasts?

scholarly journals Statistics of correlation functions in the random Heisenberg chain

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Luis A. Colmenarez ◽  
Paul A. McClarty ◽  
Masud Haque ◽  
David J. Luitz
Keyword(s):  
Correlation Functions ◽  
Heavy Tails ◽  
Probability Distributions ◽  
Many Body ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Spin Flip ◽  
Local Operators ◽  
Many Body Systems ◽  
Degenerate Perturbation Theory

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) – at least in one dimensional systems – leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder – in the thermal phase – we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in S_i^z S_{i+r}^zSizSi+rz correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the S_i^zS_{i+r}^zSizSi+rz correlator exhibits striking differences between the MBL and Anderson insulator cases.

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