A unified and universal explanation for Lévy laws and 1/f noises Export

@article{citeulike:5149230, abstract = {10.1073/pnas.0900299106 L\'{e}vy laws and 1/ noises are shown to emerge uniquely and universally from a general model of systems which superimpose the transmissions of many independent stochastic signals. The signals are considered to follow, statistically, a common—yet arbitrary—generic signal pattern which may be either stationary or dissipative. Each signal is considered to have its own random transmission amplitude and frequency. We characterize the amplitude-frequency randomizations which render the system output's stationary law and power-spectrum universal—i.e., independent of the underlying generic signal pattern. The classes of universal stationary laws and power spectra are shown to coincide, respectively, with the classes of L\'{e}vy laws and 1/ noises—thus providing a unified and universal explanation for the ubiquity of these classes of ” anomalous statistics” in various fields of science and engineering.}, author = {Eliazar, Iddo and Klafter, Joseph}, citeulike-article-id = {5149230}, citeulike-linkout-0 = {http://dx.doi.org/10.1073/pnas.0900299106}, citeulike-linkout-1 = {http://www.pnas.org/content/0900299106v1/.abstract}, citeulike-linkout-2 = {http://www.pnas.org/content/0900299106v1/.full.pdf}, citeulike-linkout-3 = {http://view.ncbi.nlm.nih.gov/pubmed/19597146}, citeulike-linkout-4 = {http://www.hubmed.org/display.cgi?uids=19597146}, day = {28}, doi = {10.1073/pnas.0900299106}, journal = {Proceedings of the National Academy of Sciences}, keywords = {frequency, noise, physics, statistics, stochastic, theory}, month = {July}, number = {30}, pages = {12251--12254}, posted-at = {2009-07-14 17:06:45}, priority = {2}, title = {A unified and universal explanation for L\'{e}vy laws and 1/f noises}, url = {http://dx.doi.org/10.1073/pnas.0900299106}, volume = {106}, year = {2009} }

TY - JOUR ID - citeulike:5149230 L3 - citeulike-article-id:5149230 N2 - 10.1073/pnas.0900299106 Lévy laws and 1/ noises are shown to emerge uniquely and universally from a general model of systems which superimpose the transmissions of many independent stochastic signals. The signals are considered to follow, statistically, a common—yet arbitrary—generic signal pattern which may be either stationary or dissipative. Each signal is considered to have its own random transmission amplitude and frequency. We characterize the amplitude-frequency randomizations which render the system output's stationary law and power-spectrum universal—i.e., independent of the underlying generic signal pattern. The classes of universal stationary laws and power spectra are shown to coincide, respectively, with the classes of Lévy laws and 1/ noises—thus providing a unified and universal explanation for the ubiquity of these classes of “anomalous statistics” in various fields of science and engineering. IS - 30 JF - Proceedings of the National Academy of Sciences EP - 12254 TI - A unified and universal explanation for Lévy laws and 1/f noises VL - 106 SP - 12251 KW - frequency KW - noise KW - physics KW - statistics KW - stochastic KW - theory AU - Eliazar, Iddo AU - Klafter, Joseph PY - 2009/07/28/ UR - http://dx.doi.org/10.1073/pnas.0900299106 ER -