Corpus ID: 211032034

Everything you wish to know about correlations but are afraid to ask

@article{Grigera2020EverythingYW,
  title={Everything you wish to know about correlations but are afraid to ask},
  author={Tom{\'a}s S. Grigera},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
  • T. Grigera
  • Published 2020
  • Computer Science, Physics
  • arXiv: Statistical Mechanics
We discuss the various definitions of time correlation functions and how to estimate them from experimental or simulation data. We start with the various definitions, both in real and in Fourier space, and explain how to extract from them a characteristic time scale. We then study how to estimate the correlation functions, i.e.\ how to obtain a good approximation to them from a sample of data obtained experimentally. Finally we discuss some practical details that arise in the actual computation… Expand

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References

SHOWING 1-10 OF 16 REFERENCES
The Theory of Critical Phenomena: An Introduction to the Renormalization Group
Here is a much-needed basic text that covers a vital area in physics for beginning graduate students. The successful calculation of critical exponents for continuous phase transitions is one of theExpand
Monte Carlo Methods
1 The general nature of Monte Carlo methods.- 2 Short resume of statistical terms.- 3 Random, pseudorandom, and quasirandom numbers.- 4 Direct simulation.- 5 General principles of the Monte CarloExpand
Spectral Analysis and Time Series
Preface. Preface to Volume 2. Contents of Volume 2. List of Main Notation. Basic Concepts. Elements of Probability Theory. Stationary Random Processes. Spectral Analysis. Estimation in the TimeExpand
Computer Simulation of Liquids
Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamicsExpand
Theory of Simple Liquids: with Applications to Soft Matter
Comprehensive coverage of topics in the theory of classical liquids Widely regarded as the standard text in its field, Theory of Simple Liquids gives an advanced but self-contained account of liquidExpand
How Nature Works: The Science of Self‐Organized Criticality
1 Complexity and Criticality.- 2 The Discovery of Self-Organized Criticality.- 3 The Sandpile Paradigm.- 4 Real Sandpiles and Landscape Formation.- 5 Earthquakes, Starquakes, and Solar Flares.- 6 TheExpand
How nature works: The science of self-organized criticality (copernicus)
Synthetic AestheticsThe Science of ScienceOn Human NatureTaking Science to SchoolThe Fairy-Land of ScienceWriting Science in Plain EnglishInformationNature of Science in Science InstructionHow NatureExpand
Statistical Physics II ( Springer , 1998 ) 7 . F . Dyson
  • 2004
in Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, ed
  • by J.L. Barrat, M. Feigelman, J. Kurchan, no. LXXVII in Les Houches Summer School (Springer,
  • 2004
G
  • Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, Oxford,
  • 1999
...
1
2
...