ICFP Stat Physics 2016

From Werner KRAUTH

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[[ICFP Stat Physics 2016 infos| Look here for practical information]] [[ICFP Stat Physics 2016 infos| Look here for practical information]]
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-==Week 1 (7 September 2016): Probability theory== 
-* [http://www.lps.ens.fr/~krauth/images/6/6d/TD01_ICFP_2016.pdf Tutorial 01: Characteristic functions / Stable distributions]  
-* [http://www.lps.ens.fr/~krauth/images/b/b4/HW01_ICFP_2016.pdf Homework 01: Chebychev inequality / Rényi formula / Lévy distribution]  
-** NB: Homework 01 will be corrected, but does not count for the final grade ("dry run"). Due on 14 September 2016, return of corrected copies: 21 September 2016. 
-** Useful program: [[renyi_problem_HW01_ICFP_2016.py| Renyi.py: Probability distribution of a sum of uniform random numbers]] 
-** Useful program: [[levy_problem_HW01_ICFP_2016.py| Levy.py: Probability distribution of a sum of random variables that may (or may not) have an infinite variance]] 
==Week 2 (14 September 2016): Statistical inference== ==Week 2 (14 September 2016): Statistical inference==
* [http://www.lps.ens.fr/~krauth/images/1/1d/TD02_ICFP_2016.pdf Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer] * [http://www.lps.ens.fr/~krauth/images/1/1d/TD02_ICFP_2016.pdf Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer]
* [http://www.lps.ens.fr/~krauth/images/9/9a/HW02_ICFP_2016.pdf Homework 02: From Maximum Likelihood to Bayes statistics] Useful program: * [http://www.lps.ens.fr/~krauth/images/9/9a/HW02_ICFP_2016.pdf Homework 02: From Maximum Likelihood to Bayes statistics] Useful program:
 +** NB: Homework 02 will be corrected, but does not count for the final grade ("dry run"). Due on 21 September 2016, return of corrected copies: 28 September 2016.
** [[bayes_tank_problem_HW02_ICFP_2016.py| Bayes_tank.py: Bayesian approach to solving the German Tank problem]] ** [[bayes_tank_problem_HW02_ICFP_2016.py| Bayes_tank.py: Bayesian approach to solving the German Tank problem]]
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* B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, 1-26, 1979. * B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, 1-26, 1979.
* P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American 248, no. 5, pp. 116-130, 1983. * P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American 248, no. 5, pp. 116-130, 1983.
 +
 +==Week 1 (7 September 2016): Probability theory==
 +* [http://www.lps.ens.fr/~krauth/images/6/6d/TD01_ICFP_2016.pdf Tutorial 01: Characteristic functions / Stable distributions]
 +* [http://www.lps.ens.fr/~krauth/images/b/b4/HW01_ICFP_2016.pdf Homework 01: Chebychev inequality / Rényi formula / Lévy distribution]
 +** NB: Homework 01 will be corrected, but does not count for the final grade ("dry run"). Due on 14 September 2016, return of corrected copies: 21 September 2016.
 +** Useful program: [[renyi_problem_HW01_ICFP_2016.py| Renyi.py: Probability distribution of a sum of uniform random numbers]]
 +** Useful program: [[levy_problem_HW01_ICFP_2016.py| Levy.py: Probability distribution of a sum of random variables that may (or may not) have an infinite variance]]
 +
 +
==Syllabus== ==Syllabus==

Revision as of 15:48, 17 September 2016

This is the homepage for the ICFP course: Statistical Physics: Concepts and Applications.

Lectures: Werner KRAUTH

Practicals & Homeworks: Maurizio FAGOTTI, Olga PETROVA

Look here for practical information

Contents

Week 2 (14 September 2016): Statistical inference

References for Week 2:

  • L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005) part 2
  • W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006) p. 58 only ;)
  • B. Efron, "Maximum likelihood and decision theory" Ann. Statist. 10, 340, 1982.
  • B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, 1-26, 1979.
  • P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American 248, no. 5, pp. 116-130, 1983.

Week 1 (7 September 2016): Probability theory


Syllabus

  • Week 1: Probability theory
    • Probabilities, probability distributions, sampling
    • Random variables
    • Expectations
    • Inequalities (Markov, Chebychev, Hoeffding)
    • Convergence of random variables (Laws of large numbers, CLT)
    • Lévy distributions
  • Week 2: Statistics (statistical inference, estimation, learning)
    • Point estimation, confidence intervals
    • Bootstrap
    • Method of moments
    • Maximum likelihood, Fisher information
    • Parametric Bootstrap
    • Bayes statistics
  • Week 3: Statistical mechanics and Thermodynamics
    • Rapid overview on the connection between statistical mechanics and thermodynamics
    • lightning review of ensembles and
    • lightning review of the main physical quantities (partition function, energy, free energy, entropy, chemical potential, correlation functions, etc).
  • Week 4: Physics in one dimension
    • One-dimensional hard spheres, virial expansion, partition function
    • One-dimensional Ising model
    • Transfer matrix
    • Kittel model
    • ~Chui-Weeks model: Infinite-dimensional transfer matrix
    • One-dimensional Ising model with 1/r^2 interactions
  • Week 5: Two-dimensional Ising model: From Ising to Onsager
    • Peierls argument, ~Kramers-Wannier relation
    • Two-dimensional transfer matrix (following Schultz et al)
    • ~Jordan-Wigner transformation
    • Free energy calculation
    • Spontaneous magnetization, zero-field susceptibility
    • Kaufman, ~Ferdinand-Fisher, Beale
  • Week 6: Two-dimensional Ising model: From Kac and Ward to Saul and Kardar
    • Van der Waerden, low-temperature and high-temperature expansions
    • Duality
  • Week 7: Physics in two dimensions (~Kosterlitz-Thouless physics): XY (planar rotor) model
    • Peierls argument
    • ~Mermin-Wagner theorem
    • Non-universality
  • Week 8: Physics in two dimensions (~Kosterlitz-Thouless physics): Particle systems, superfluids
  • Week 09: Physics in infinite dimensions: Mean-field theory, Scaling
  • Week 10: Physics in infinite dimensions: Landau theory
  • Week 11: Renormalization group
  • Week 12: The Solid state: Order parameters, correlation functions
  • Week 13: Quantum systems - bosons.
  • Week 14: Quantum systems - spin systems
  • Week 15: Equilibrium and transport, Fluctuation-dissipation theorem.

References

Lecture notes will be available before each course.

Books

  • L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005)
  • W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006)
  • M Plischke, B Bergersen, "Equilibrium Statistical Physics" (World Scientific)
  • L. D. Landau, E. M. Lifshitz, "Statistical Physics" (Pergamon)
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