Single-big-jump principle in physical modeling
Physical Review E, ISSN: 2470-0053, Vol: 100, Issue: 1, Page: 012108
2019
- 71Citations
- 17Captures
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Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Metrics Details
- Citations71
- Citation Indexes71
- 71
- CrossRef1
- Captures17
- Readers17
- 17
Article Description
The big-jump principle is a well-established mathematical result for sums of independent and identically distributed random variables extracted from a fat-tailed distribution. It states that the tail of the distribution of the sum is the same as the distribution of the largest summand. In practice, it means that when in a stochastic process the relevant quantity is a sum of variables, the mechanism leading to rare events is peculiar: Instead of being caused by a set of many small deviations all in the same direction, one jump, the biggest of the lot, provides the main contribution to the rare large fluctuation. We reformulate and elevate the big-jump principle beyond its current status to allow it to deal with correlations, finite cutoffs, continuous paths, memory, and quenched disorder. Doing so we are able to predict rare events using the extended big-jump principle in Lévy walks, in a model of laser cooling, in a scattering process on a heterogeneous structure, and in a class of Lévy walks with memory. We argue that the generalized big-jump principle can serve as an excellent guideline for reliable estimates of risk and probabilities of rare events in many complex processes featuring heavy-tailed distributions, ranging from contamination spreading to active transport in the cell.
Bibliographic Details
American Physical Society (APS)
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