نظرية التخلل

نظرية التخلل Percolation theory (أو نظرية التطعيم) في الرياضيات سلوك العقد المتصلة في خط بياني عشوائي. تشمل تطبيقات هذه النظرية بشكل أساسي مجال علوم المواد الهندسية وبالإضافة إلى مجالات أخرى تتعلق بالترشيح.

وترتبط هذه النظرية بالنظرية الكسيرية Fractal.

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مقدمة

A three-dimensional site percolation graph

Detail of a bond percolation on the square lattice in two dimensions with percolation probability

p = 0.51

انظر أيضاً

References

للاستزادة

Aizenman, Michael; Barsky, David (1987), "Sharpness of the phase transition in percolation models", Communications in Mathematical Physics 108 (3): 489–526, doi:10.1007/BF01212322, Bibcode: 1987CMaPh.108..489A
Bollobás, Béla; Riordan, Oliver (2006), Percolation, Cambridge University Press, ISBN 978-0521872324, http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521872324
Broadbent, Simon; Hammersley, John (1957), "Percolation processes I. Crystals and mazes", Proceedings of the Cambridge Philosophical Society 53 (3): 629–641, doi:10.1017/S0305004100032680, Bibcode: 1957PCPS...53..629B
Bunde A. and Havlin S. (1996), Fractals and Disordered Systems, Springer, http://havlin.biu.ac.il/Shlomo%20Havlin%20books_fds.php
Cohen R. and Havlin S. (2010), Complex Networks: Structure, Robustness and Function, Cambridge University Press, http://havlin.biu.ac.il/Shlomo%20Havlin%20books_com_net.php
Grimmett, Geoffrey (1999), Percolation, Springer, http://www.statslab.cam.ac.uk/~grg/papers/perc/perc.html
Grimmett, Geoffrey; Marstrand, John (1990), "The supercritical phase of percolation is well behaved", Proceedings of the Royal Society A 430 (1879): 439–457, doi:10.1098/rspa.1990.0100, Bibcode: 1990RSPSA.430..439G
Hara, Takashi; Slade, Gordon (1990), "Mean-field critical behaviour for percolation in high dimensions", Communications in Mathematical Physics 128 (2): 333–391, doi:10.1007/BF02108785, Bibcode: 1990CMaPh.128..333H
Kesten, Harry (1982), Percolation theory for mathematicians, Birkhauser
Menshikov, Mikhail (1986), "Coincidence of critical points in percolation problems", Soviet Mathematics - Doklady 33: 856–859
Smirnov, Stanislav (2001), "Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits", Comptes Rendus de l'Académie des Sciences 333 (3): 239–244, doi:10.1016/S0764-4442(01)01991-7, Bibcode: 2001CRASM.333..239S
Stauffer, Dietrich; Aharony, Anthony (1994), Introduction to Percolation Theory (2nd ed.), CRC Press, ISBN 978-0-7484-0253-3

وصلات خارجية

PercoVIS: a Mac OS X program to visualize percolation on networks in real time
Interactive Percolation
Kesten, Harry (May 2006), "What Is ... Percolation?" (PDF), Notices of the American Mathematical Society 53 (5): 572–573, ISSN 1088-9477, http://www.ams.org/notices/200605/what-is-kesten.pdf
Austin, David (July 2008), Percolation: Slipping through the Cracks, American Mathematical Society, http://www.ams.org/featurecolumn/archive/percolation.html
Nanohub online course on Percolation Theory
Introduction to Percolation Theory: short course by Shlomo Havlin

v t e عمليات تصادفية
Discrete time	Bernoulli process Branching process Chinese restaurant process Galton–Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding
Continuous time	Bessel process Birth–death process Brownian motion Bridge Excursion Fractional Geometric Meander Cauchy process Contact process Cox process Diffusion process Empirical process Feller process Fleming–Viot process Gamma process Hunt process Interacting particle systems Itō diffusion Itō process Jump diffusion Jump process Lévy process Local time Markov additive process McKean–Vlasov process Ornstein–Uhlenbeck process Poisson process Compound Non-homogeneous Point process Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph process Variance gamma process Wiener process Wiener sausage
Both	Branching process Gaussian process Hidden Markov model (HMM) Markov process Martingale Differences Local Sub- Super- Random dynamical system Regenerative process Renewal process White noise
حقول وأخرى	Dirichlet process Gaussian random field Gibbs measure Hopfield model Ising model Markov random field Percolation Pitman–Yor process Point process Cox Poisson Potts model Random field Random graph
نماذج متسلسلات زمنية	Autoregressive conditional heteroskedasticity (ARCH) model Autoregressive integrated moving average (ARIMA) model Autoregressive (AR) model Autoregressive–moving-average (ARMA) model Generalized autoregressive conditional heteroskedasticity (GARCH) model Moving-average (MA) model
نماذج مالية	بلاك-درمان-توي بلاك-كاراسينسكي بلاك-شولز تشـِن Constant elasticity of variance (CEV) Cox–Ingersoll–Ross (CIR) Garman–Kohlhagen Heath–Jarrow–Morton (HJM) هستون هو–لي هل–وايت LIBOR market SABR volatility Vašícek
Actuarial models	Bühlmann Cramér–Lundberg Risk process Sparre–Anderson
Queueing models	Bulk Fluid Generalized queueing network M/G/1 M/M/1 M/M/c
الخصائص	Càdlàg paths Continuous Continuous paths Ergodic Exchangeable Feller-continuous Gauss–Markov Markov Mixing Piecewise deterministic Predictable Progressively measurable Self-similar Stationary Time-reversible
نظريات الحد	Central limit theorem Donsker's theorem Doob's martingale convergence theorems Ergodic theorem Fisher–Tippett–Gnedenko theorem Large deviation principle Law of large numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem
Inequalities	Burkholder–Davis–Gundy Doob's martingale Kunita–Watanabe
أدوات	صيغة كاميرون-مارتن Convergence of random variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal generator Itō integral Itō's lemma Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric Malliavin calculus Martingale representation theorem Optional stopping theorem Prohorov theorem Quadratic variation Reflection principle Skorokhod integral Skorokhod's representation theorem Skorokhod space Snell envelope Stochastic differential equation Tanaka Stopping time Stratonovich integral Uniform integrability Usual hypotheses Wiener space Classical Abstract
تخصصات	Actuarial mathematics Econometrics Ergodic theory Extreme value theory (EVT) Large deviations theory Mathematical finance Mathematical statistics Probability theory Queueing theory Renewal theory Ruin theory Statistics Stochastic analysis Time series analysis تعلم آلي
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