On the wedding of certain dynamical processes in disordered complex materials to the theory of stable (Lévy) distribution functions

1983 ◽  
pp. 109-137 ◽  
Author(s):  
Elliott W. Montroll ◽  
Michael F. Shlesinger
Keyword(s):  
Distribution Functions ◽  
Complex Materials ◽  
Dynamical Processes ◽  
Lévy Distribution ◽  
Levy Distribution

scholarly journals Observation of Lévy distribution and replica symmetry breaking in random lasers from a single set of measurements

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Anderson S. L. Gomes ◽  
Ernesto P. Raposo ◽  
André L. Moura ◽  
Serge I. Fewo ◽  
Pablo I. R. Pincheira ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Random Lasers ◽  
Lévy Distribution ◽  
Levy Distribution ◽  
Single Set

scholarly journals Simulations of Lévy walk

2020 ◽  
Author(s):  
Venkat Abhignan ◽  
Sinduja Rajadurai
Keyword(s):  
Movement Pattern ◽  
Stable Distributions ◽  
Lévy Distribution ◽  
Lévy Walk ◽  
Lévy Walks ◽  
Levy Distribution ◽  
Levy Walk ◽  
The Ideal

AbstractWe simulate stable distributions to study the ideal movement pattern for the spread of a virus using autonomous carrier. We observe Lévy walks to be the most ideal way to spread and further study how the parameters in Lévy distribution affects the spread.

scholarly journals Econophysics and Fractional Calculus: Einstein’s Evolution Equation, the Fractal Market Hypothesis, Trend Analysis and Future Price Prediction

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1057 ◽  
Author(s):  
Jonathan Blackledge ◽  
Derek Kearney ◽  
Marc Lamphiere ◽  
Raja Rani ◽  
Paddy Walsh
Keyword(s):  
Fractional Calculus ◽  
Evolution Equation ◽  
Fractional Diffusion ◽  
Future Price ◽  
Impulse Response Functions ◽  
Scattering Problems ◽  
Stochastic Fields ◽  
Lévy Distribution ◽  
Levy Distribution ◽  
Fractal Market Hypothesis

This paper examines a range of results that can be derived from Einstein’s evolution equation focusing on the effect of introducing a Lévy distribution into the evolution equation. In this context, we examine the derivation (derived exclusively from the evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov–Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent and volatility. In this way, we provide a collection of results (which includes the derivation of certain fractional partial differential equations) that are fundamental to the stochastic modelling associated with elastic scattering problems obtained under a unifying theme, i.e., Einstein’s evolution equation. This includes an analysis of stochastic fields governed by a symmetric (zero-mean) Gaussian distribution, a Lévy distribution characterised by the Lévy index γ ∈ [ 0 , 2 ] and the derivation of two impulse response functions for each case. The relationship between non-Gaussian distributions and fractional calculus is examined and applications to financial forecasting under the fractal market hypothesis considered, the reader being provided with example software functions (written in MATLAB) so that the results presented may be reproduced and/or further investigated.

scholarly journals Comparing Multicomponent Erlang Distribution and Lévy Distribution of Particle Transverse Momentums

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hua-Rong Wei ◽  
Ya-Hui Chen ◽  
Li-Na Gao ◽  
Fu-Hu Liu
Keyword(s):  
Hadron Collider ◽  
Center Of Mass ◽  
Heavy Ion ◽  
Erlang Distribution ◽  
Relativistic Heavy Ion Collider ◽  
Final State ◽  
Heavy Particles ◽  
Proton Proton ◽  
Lévy Distribution ◽  
Levy Distribution

The transverse momentum spectrums of final-state products produced in nucleus-nucleus and proton-proton collisions at different center-of-mass energies are analyzed by using a multicomponent Erlang distribution and the Lévy distribution. The results calculated by the two models are found in most cases to be in agreement with experimental data from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The multicomponent Erlang distribution that resulted from a multisource thermal model seems to give a better description as compared with the Lévy distribution. The temperature parameters of interacting system corresponding to different types of final-state products are obtained. Light particles correspond to a low temperature emission, and heavy particles correspond to a high temperature emission. Extracted temperature from central collisions is higher than that from peripheral collisions.

Towards Swarm Diversity: Random Sampling in Variable Neighborhoods Procedure Using a Lévy Distribution

2014 ◽  
Vol 18 (1) ◽  
Author(s):  
Gonzalo Nápoles Ruiz ◽  
Isel Grau García ◽  
Marilyn Bello García ◽  
Rafael Bello Pérez
Keyword(s):  
Random Sampling ◽  
Lévy Distribution ◽  
Levy Distribution

scholarly journals Lévy distribution in many-particle quantum systems

2010 ◽  
Vol 81 (4) ◽  
Author(s):  
A. V. Ponomarev ◽  
S. Denisov ◽  
P. Hänggi
Keyword(s):  
Quantum Systems ◽  
Lévy Distribution ◽  
Levy Distribution
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