Random Processes  

Randomness in General > s.a. probability.
* Idea: A random variable is a variable with values in a measurable space, whose value is determined by an underlying random experiment.
* Quantum random number generators: A simple general procedure is to measure a quantum system in a basis complementary to its preparation.
@ General references: Compagner AJP(91)aug [definitions]; Bennett 99 [history]; Eagle BJPS(05) [as unpredictability]; Shkliarevsky a1104 [randomness and determinism]; Zenil ed-11 [and computation].
@ Random numbers: Vattulainen et al PRL(94) [tests]; Wei & Guo OL(09)-a0905, Guo et al PRE(10)-a0908 [true random number generator]; Reidler et al PRL(09) + news sn(09)jul [generator based on chaotic semiconductor laser]; Svozil LNCS(14)-a1406 [oracles of randomness]; Bierhorst et al a1702 [certified by the impossibility of superluminal signaling].
@ Quantum random number generators: Stefanov et al qp/99; Svozil PRA(09)-a0903; Pironio et al Nat(10)apr-a0911 [certified by Bell-inequality violation] + news pw(10)apr; Liu et al a1006; Stipčević SPIE(12)-a1103 [and cryptography]; Frauchiger et al a1311; Thinh et al PRA(16)-a1601 [2-level system in a relativistic quantum field]; Cao et al PRX(16) [source-independent scheme]; Herrero-Collantes & García-Escartin RMP(17)-a1604 [rev].
@ In physics: Svozil in(11)-a0905; Dhara et al PRL(14) [quantum processes with fully intrinsic randomness]; Svozil a1405 [sources of physical indeterminism]; Khrennikov a1512 [quantum vs classical]; Khrennikov 16.
@ Related topics: Dodson a0811-conf [quantifying departures from randomness for point distributions]; Müller et al CMP(12)-a1107 [randomization and entanglement in general probabilistic theories]; Scarani a1501-proc [Thomas Aquinas' position]; > s.a. Determinism; functions.

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 sequences themselves (Bernoulli chain/sequence).
* Examples: No computable number is random (see π).
* 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; Matthews et al a1312 [randomness test using photons]; Lifshits 14 [by example].
> Special types, applications: see Bertrand's Paradox; 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; realism; 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]; Volovich FP(11) [in classical mechanics].
@ 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 NJP(10)-a0811 [and logical independence]; Calude et al a0912 [quantum vs computable sources of (pseudo)randomness], PRA(10) [experimental evidence of quantum randomness incomputability]; Rogers a1008 [quantum measurements cannot be proved random]; García Álvarez IJMPD(11)-a1011-fs [and Feynman's paths]; Gallego et al nComm(13)-a1210; Brandão et al PRL(16)-a1605 [quantum pseudorandomness from random quantum circuits]; Bera et al a1611 [non-technical].
@ Random tensors: Gurau a1110 [universality results]; Gurau Sigma(16)-a1609 [overview]; > s.a. matrices.
@ Geometry, combinatorics: Ferrari et al PLA(11)-a1107 [random metrics]; > s.a. 3D geometries; dynamical triangulations [including surfaces]; regge calculus; statistical geometry; types of graphs.

Random Fields > s.a. electricity [random dipoles]; modified formulations of QED [Random Electrodynamics].
@ General references: Adler 81; Bertschinger ApJS(01)ap [multiscale simulation package]; de Dominicis & Giardina 06; Adler & Taylor 07 [and geometry]; Vanmarcke 10; Vargas Le-Bert a1507 [construction of physically relevant functional measures].
@ 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].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 11 jun 2017