Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement
The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1317 |
| _version_ | 1797547530471342080 |
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| author | Aleksander Stanislavsky Aleksander Weron |
| author_facet | Aleksander Stanislavsky Aleksander Weron |
| author_sort | Aleksander Stanislavsky |
| collection | DOAJ |
| description | The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not Laplace distributed. We discovered a new mechanism leading to the Laplace distribution of observable values. This mechanism changes the contribution ratio between a jump and a continuous parts of random processes. Our concept uses properties of Bernstein functions and subordinators connected with them. |
| first_indexed | 2024-03-10T14:45:22Z |
| format | Article |
| id | doaj.art-f192eef47101418ca42de2fb214a15a0 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T14:45:22Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f192eef47101418ca42de2fb214a15a02023-11-20T21:27:14ZengMDPI AGEntropy1099-43002020-11-012211131710.3390/e22111317Look at Tempered Subdiffusion in a Conjugate Map: Desire for the ConfinementAleksander Stanislavsky0Aleksander Weron1Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wroclaw, PolandFaculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wroclaw, PolandThe Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not Laplace distributed. We discovered a new mechanism leading to the Laplace distribution of observable values. This mechanism changes the contribution ratio between a jump and a continuous parts of random processes. Our concept uses properties of Bernstein functions and subordinators connected with them.https://www.mdpi.com/1099-4300/22/11/1317anomalous diffusionstatistical analysissingle-particle trackingtrajectory classification |
| spellingShingle | Aleksander Stanislavsky Aleksander Weron Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement Entropy anomalous diffusion statistical analysis single-particle tracking trajectory classification |
| title | Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement |
| title_full | Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement |
| title_fullStr | Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement |
| title_full_unstemmed | Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement |
| title_short | Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement |
| title_sort | look at tempered subdiffusion in a conjugate map desire for the confinement |
| topic | anomalous diffusion statistical analysis single-particle tracking trajectory classification |
| url | https://www.mdpi.com/1099-4300/22/11/1317 |
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