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Transition in the decay rates of stationary distributions of Levy motion in an energy landscape
The time evolution of random variables with Lévy statistics has the ability to develop jumps, displaying very different behaviors from continuously fluctuating cases. Such patterns appear in an ever broadening range of examples including random lasers, non-Gaussian kinetics, or foraging strategies....
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| Format: | Default Article |
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2016
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| Online Access: | https://hdl.handle.net/2134/18655 |
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| _version_ | 1818172689373724672 |
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| author | Kamil Kaleta Jozsef Lorinczi |
| author_facet | Kamil Kaleta Jozsef Lorinczi |
| author_sort | Kamil Kaleta (7159700) |
| collection | Figshare |
| description | The time evolution of random variables with Lévy statistics has the ability to develop jumps, displaying very different behaviors from continuously fluctuating cases. Such patterns appear in an ever broadening range of examples including random lasers, non-Gaussian kinetics, or foraging strategies. The penalizing or reinforcing effect of the environment, however, has been little explored so far. We report a new phenomenon which manifests as a qualitative transition in the spatial decay behavior of the stationary measure of a jump process under an external potential, occurring on a combined change in the characteristics of the process and the lowest eigenvalue resulting from the effect of the potential. This also provides insight into the fundamental question of what is the mechanism of the spatial decay of a ground state. |
| format | Default Article |
| id | rr-article-9388640 |
| institution | Loughborough University |
| publishDate | 2016 |
| record_format | Figshare |
| spelling | rr-article-93886402016-02-24T00:00:00Z Transition in the decay rates of stationary distributions of Levy motion in an energy landscape Kamil Kaleta (7159700) Jozsef Lorinczi (1258137) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified The time evolution of random variables with Lévy statistics has the ability to develop jumps, displaying very different behaviors from continuously fluctuating cases. Such patterns appear in an ever broadening range of examples including random lasers, non-Gaussian kinetics, or foraging strategies. The penalizing or reinforcing effect of the environment, however, has been little explored so far. We report a new phenomenon which manifests as a qualitative transition in the spatial decay behavior of the stationary measure of a jump process under an external potential, occurring on a combined change in the characteristics of the process and the lowest eigenvalue resulting from the effect of the potential. This also provides insight into the fundamental question of what is the mechanism of the spatial decay of a ground state. 2016-02-24T00:00:00Z Text Journal contribution 2134/18655 https://figshare.com/articles/journal_contribution/Transition_in_the_decay_rates_of_stationary_distributions_of_Levy_motion_in_an_energy_landscape/9388640 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified Kamil Kaleta Jozsef Lorinczi Transition in the decay rates of stationary distributions of Levy motion in an energy landscape |
| title | Transition in the decay rates of stationary distributions of Levy motion in an energy landscape |
| title_full | Transition in the decay rates of stationary distributions of Levy motion in an energy landscape |
| title_fullStr | Transition in the decay rates of stationary distributions of Levy motion in an energy landscape |
| title_full_unstemmed | Transition in the decay rates of stationary distributions of Levy motion in an energy landscape |
| title_short | Transition in the decay rates of stationary distributions of Levy motion in an energy landscape |
| title_sort | transition in the decay rates of stationary distributions of levy motion in an energy landscape |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/18655 |