Extremal regime for one-dimensional Mott variable-range hopping
[Régime extrémal pour la marche aléatoire de Mott en dimension un]
Croydon, David A.1 ; Fukushima, Ryoki2 ; Junk, Stefan3
1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606–8502, Japan
2 Institute of Mathematics, University of Tsukuba, 1–1–1 Tennodai, Tsukuba 305–8571, Ibaraki, Japan
3 Advanced Institute for Materials Research, Tohoku University, 2–1–1 Katahira, Aoba-ku, Sendai 980–8577, Japan
Annales Henri Lebesgue, Tome 6 (2023), pp. 1169-1211

We study the asymptotic behaviour of a version of the one-dimensional Mott random walk in a regime that exhibits severe blocking. We establish that, for any fixed time, the appropriately-rescaled Mott random walk is situated between two environment-measurable barriers, the locations of which are shown to have an extremal scaling limit. Moreover, we give an asymptotic description of the distribution of the Mott random walk between the barriers that contain it.

Nous étudions le comportement asymptotique d’une version de la marche aléatoire de Mott en dimension un, dans un régime où un phénomène aigu de bloquage a lieu. Nous établissons que, pour tout temps fixé, la marche aléatoire de Mott correctement redimensionnée se situe entre deux barrières mesurables en fonction de l’environnement. L’emplacement de ces barrières présente une limite d’échelle qui s’exprime en termes de processus extrémaux. Nous donnons également une description asymptotique de la distribution de la marche aléatoire de Mott entre les barrières qui la contiennent.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/ahl.186
Classification : 60K37, 60F17, 60G70, 60J27, 82A41, 82D30
Keywords: random walk in random environment, disordered media, sub-diffusivity, Mott variable-range hopping, extremal process

Croydon, David A. 1 ; Fukushima, Ryoki 2 ; Junk, Stefan 3

1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606–8502, Japan
2 Institute of Mathematics, University of Tsukuba, 1–1–1 Tennodai, Tsukuba 305–8571, Ibaraki, Japan
3 Advanced Institute for Materials Research, Tohoku University, 2–1–1 Katahira, Aoba-ku, Sendai 980–8577, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Extremal regime for one-dimensional {Mott} variable-range hopping},
     journal = {Annales Henri Lebesgue},
     pages = {1169--1211},
     year = {2023},
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     volume = {6},
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     language = {en},
     url = {https://www.numdam.org/articles/10.5802/ahl.186/}
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Croydon, David A.; Fukushima, Ryoki; Junk, Stefan. Extremal regime for one-dimensional Mott variable-range hopping. Annales Henri Lebesgue, Tome 6 (2023), pp. 1169-1211. doi: 10.5802/ahl.186

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