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.
* Quantum randomness in general: Entanglement can be used as a resource for the generation of certifiable randomness, since it leads to violations of the Bell inequalities, and these in turn imply that measurement outcomes are not the result of an underlying deterministic process.
@ 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]; Banchi et al PRX(17) [from interacting many-body systems]; Martínez et al a1810 [tests].
@ 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; Woodhead et al a1901 [using entanglement as a resource].
@ 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: Grimmett 18 [on graphs and lattices]; > s.a. 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].


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