Random Processes

Randomness in General > s.a. matrices; probability.
@ General references: Shale JFA(79) [functions]; Compagner AJP(91)aug [definitions]; Bennett 98 [history]; Eagle BJPS(05) [as unpredictability]; Svozil a0905-in [in physics].
@ Random numbers: Vattulainen et al PRL(94) [tests]; Stefanov et al qp/99 [generators, using quantum mechanics]; Svozil PRA(09)-a0903 [quantum]; Wei & Guo a0905, Guo et al a0908 [true random number generator]; Reidler et al PRL(09) + news sn(09)jul [generator based on chaotic semiconductor laser]; Pironio et al a0911 [certified by Bell-inequality violation].
@ Related topics: Dodson a0811-in [quantifying departures from randomness for point distributions].

Random Process > s.a. computing; Fiber [fiber process]; stochastic processes.
* Idea: (The most) random (infinite) sequences are those which cannot be described by algorithms shorter than the sequances themselves (Bernoulli chain/sequence).
* Examples: No computable number is random (see ).
* Remark: It is impossible to prove that any given sequence was generated by a random process.
@ References: Zeldovich et al 90; Ochs Nat(90)jan, Yockey Nat(90)apr; Chaitin NS(90)mar.
> Special types, applications: see fractals; random walk [including quantum walk]; statistical geometry [Poisson and other point processes].

Other Random Systems > s.a. chaos; ising models; lattice field theory; quantum klein-gordon fields; scattering.
@ General references: Grandy FP(92) [thermodynamics]; Svozil 93; Mézard cm/95-ln [replica field theory]; Drozdz & Wojcik nt/00 [emergence of order]; Mulhall et al PRL(00)nt [randomly interacting spins]; Donetti & Destri JPA(04) [scale-free random trees].
@ Random medium: Lima et al PRL(01) [deterministic walk]; > s.a. quantum particle; Transport Phenomena; wave phenomena.
@ In dynamics: Ornstein 74; Gaspard & Wang PRP(93); Johnson et al PRL(98) [and orderly spectra]; Clifford & Stirzaker PRS(08) [history-dependent].
@ In quantum mechanics: Yurtsever qp/98 [algorithmic randomness]; Ulfbeck & Bohr FP(01) ["genuine fortuitousness"]; de la Torre EJP(08)-a0707; Paterek et al a0811 [and undecidability].
> Geometry, combinatorics: see dynamical triangulations [including surfaces], regge calculus; statistical geometry; types of graphs.

Random Fields > s.a. electricity [random dipoles].
@ General references: Bertschinger ApJS(01)ap [multiscale simulation package]; de Dominicis & Giardina 06 [r JSP(07)].
@ Related topics: Vojta JPA(97), JPA(97) [damage spreading, Ising model].

Other Related Issues
@ Interpolation of randomly-sampled data: Lombardi & Schneider A&A(02)ap [in astronomy].

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send feedback and suggestions to bombelli at olemiss.edu – modified 18 nov 2009