publication . Part of book or chapter of book . Preprint . 2001

Monte Carlo basics

James Gubernatis; Naoki Kawashima; Philipp Werner;
  • Published: 12 Apr 2001
  • Publisher: Cambridge University Press
An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers, central limit theorem (stable distribution, Levy distribution), random numbers (generation and testing), random sampling techniques (inversion, rejection, sampling from a Gaussian, Metropolis sampling), analogue Monte Carlo and Importance sampling (exponential biasing, spanier technique).
free text keywords: Monte Carlo method, Physics, Dynamic Monte Carlo method, Monte Carlo method in statistical physics, Monte Carlo molecular modeling, Statistical physics, Condensed Matter - Statistical Mechanics
31 references, page 1 of 3

[1] A. Hall, On an experimental determination of π, Messeng. Math., 2, 113 (1873).

[2] Francis Galton, Natural Inheritance (1989), cited in M. Cundy and A. P. Rollet, Mathematical Models, Oxford University Press, Oxford (1961).

[4] P. C. Mahalanobis, Dialectica 8, 95 (1954), cited in [5].

[11] M. C. Valsakumar, Unpublished notes (1990).

[12] P. L´evy, Calcul des Probabilit´es, Gauthier Villars, Paris (1925); P. L´evy, Th´eorie de l'addition des variables al´etoires, Gauthier Villars, Paris (1937); for a proof in English of the L´evy stable law, see, A. N. Gnedenko and V. N. Kolmogrov, Limit Distributions for Sums of Random Variables, Reading MA, Addison-Wesley (1954).

[15] T. M. John and K. P. N. Murthy, J. Statis. Phys. 45 , 753 (1986).

[16] L. Szilard, Z. Phys. 530, 840 (1929); L. Brillouin, J. Appl. Phys., 22, 334 (1951); R. Landauer, IBM J. Res. Dev., 5, 183 (1960); R. J. Solomonoff, Inf. Control, 7,1 (1964); A. N. Kolmogrov, IEEE Trans. Inf. Theor., 1, 3 (1965); G. J. Chaitin, J. Assoc. Comput. Mach., 13, 547 (1966). A. Wehrl, Rev. Mod. Phys., 50, 221 (1978); C. H. Bennet, Int. J. Theor. Phy., 12, 905 (1982); K. G. Denbigh and J. S.Denbigh, Entropy in relation to incomplete knowledge, Cambridge University Press, Cambridge, U.K. (1985); P. C. W. Davies, Physics of Time Assymetry, Univ. California Press, Berkeley (1985); G. J. Chaitin, Information, Randomness and Incompleteness: papers on Algorithmic information theory, World Scientific, Singapore (1987)(a collection of Chaitin's papers). C. H. Bennet, IBM J. Res. Dev., 32, 16 (1988); R. Landauer, Nature, 335, 779 (1988); W. H. Zurek, Phys. Rev., A40, 4731 (1989); W. H. Zurek, Phys. Rev. A40, 4731 (1989); I. Prigogine, From Being to Becoming, Freeman, San Francisco (1990). C. M. Caves, Phys. Rev. Lett., 64, 2111 (1990); C. M. Caves, W. G. Unruh and W. Zurek, Phys. Rev. Lett., 65, 1387 (1990); W. H. Zurek (Ed.), Complexity, Entropy and the Physics of Information, Vol. VIII of Santa Fe Institute Studies in the Sciences of Complexity, Addison Wesley (1990); C. H. Bennet, Sci. Am. 275, 106 (1997).

[17] N. A. Friggario and N. Clark, Trans. Amer. Nucl. Soc., 22, 283 (1975); N. A. Friggario and N. Clark, Toward Truly Random Numbers, Report ANL/ES-26 Part 4, Argonne National Laboratory (1978).

[21] J. H. Ahren, U. Dieter and A. Grube, Computing, 6, 121 (1970); D. Knuth, The art of computer Programming, Vol. 2, Reading Mass.: Addison Wesley (1969); J. C. Butcher, Math. Comp., 15, 198 (1961).

[22] G. Marsaglia, Proc. Nat. Acad. Sci., 61, 25 (1968); G. Marsaglia, Applications of Number Theory to Numerical Analysis, Academic, New York (1972).

[23] I. Vattulainen, K. Kanakaala, J. Saarinen, and T. Ala-Nissila, Comp. Phys. Commun., 86, 209 (1995).

[24] F. Gutbrod, New trends in pseudo random number generation, Annual Reviews of Computational Physics VI, World Scientific (to be published); G. Marsaglia, A Current View of Random Number Generators, in Proc. Computer Science and Statistics, Sixteenth Symp. on Interface, Elsevier (1985); G. Marsaglia and A. Zaman, Ann. Appl. Probability, 1, 462 (1991).

[25] A. Bonelli and S. Ruffo, Modular Transformations, Order-Chaos Transitions and Pseudo-Random Number Generation, Int. J. Mod. Phys., C9(4)(1998).

[26] D. H. Lehmer, Ann. Comp. Lab. Harvard Univ., 26, 141 (1951).

[27] M. Greenberger, Math. Comp., 15, 383 (1961); M. Greenberger, Comm. ACM, 8, 177 (1965).

31 references, page 1 of 3
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Part of book or chapter of book . Preprint . 2001

Monte Carlo basics

James Gubernatis; Naoki Kawashima; Philipp Werner;