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For:
Barlow MT
, Černý J.
Convergence to fractional kinetics for random walks associated with unbounded conductances.
Probab Theory Relat Fields
2009. [DOI:
10.1007/s00440-009-0257-z
]
[
Citation(s) in
RCA
: 30
]
[
Impact Index Per Article: 2.0
]
[
Reference Citation Analysis
]
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[Indexed: 11/27/2022]
Number
Cited by Other Article(s)
1
Du Q
, Toniazzi L, Zhou Z. Stochastic representation of solution to nonlocal-in-time diffusion.
Stoch Process Their Appl
2020. [DOI:
10.1016/j.spa.2019.06.011
]
[
Citation(s) in
RCA
: 8
]
[
Impact Index Per Article: 2.0
]
[
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]
[
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[Indexed: 10/26/2022]
Abstract
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2
Berry–Esseen estimates for regenerative processes under weak moment assumptions.
Stoch Process Their Appl
2019. [DOI:
10.1016/j.spa.2018.05.001
]
[
Citation(s) in
RCA
: 1
]
[
Impact Index Per Article: 0.2
]
[
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]
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[Indexed: 11/20/2022]
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3
Fribergh A
, Kious D. Scaling limits for sub-ballistic biased random walks in random conductances.
ANN PROBAB
2018. [DOI:
10.1214/16-aop1159
]
[
Citation(s) in
RCA
: 5
]
[
Impact Index Per Article: 0.8
]
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[Indexed: 11/19/2022]
Abstract
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4
Croydon D
, Hambly B, Kumagai T. Time-changes of stochastic processes associated with resistance forms.
ELECTRON J PROBAB
2017. [DOI:
10.1214/17-ejp99
]
[
Citation(s) in
RCA
: 8
]
[
Impact Index Per Article: 1.1
]
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[Indexed: 11/19/2022]
Abstract
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5
Chen X
. Gaussian bounds and collisions of variable speed random walks on lattices with power law conductances.
Stoch Process Their Appl
2016. [DOI:
10.1016/j.spa.2016.03.011
]
[
Citation(s) in
RCA
: 0
]
[
Impact Index Per Article: 0
]
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[Indexed: 10/21/2022]
Abstract
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6
Černý J
, Wassmer T. Aging of the Metropolis dynamics on the random energy model.
Probab Theory Relat Fields
2015. [DOI:
10.1007/s00440-015-0681-1
]
[
Citation(s) in
RCA
: 11
]
[
Impact Index Per Article: 1.2
]
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[Indexed: 10/22/2022]
Abstract
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7
Randomly trapped random walks on
Z
d
.
Stoch Process Their Appl
2015. [DOI:
10.1016/j.spa.2014.10.002
]
[
Citation(s) in
RCA
: 6
]
[
Impact Index Per Article: 0.7
]
[
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]
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[Indexed: 11/24/2022]
Abstract
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8
Fontes LRG
, Gava RJ, Gayrard V. The K-process on a tree as a scaling limit of the GREM-like trap model.
ANN APPL PROBAB
2014. [DOI:
10.1214/13-aap937
]
[
Citation(s) in
RCA
: 3
]
[
Impact Index Per Article: 0.3
]
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[Indexed: 11/19/2022]
Abstract
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9
Long-range Trap Models on $$\mathbb {Z}$$ Z and Quasistable Processes.
J THEOR PROBAB
2014. [DOI:
10.1007/s10959-014-0548-x
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.2
]
[
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[Indexed: 11/25/2022]
Abstract
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10
Mathieu P
, Mourrat JC. Aging of asymmetric dynamics on the random energy model.
Probab Theory Relat Fields
2014. [DOI:
10.1007/s00440-014-0551-2
]
[
Citation(s) in
RCA
: 4
]
[
Impact Index Per Article: 0.4
]
[
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[Indexed: 10/25/2022]
Abstract
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11
Meerschaert MM
, Nane E, Xiao Y. FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS.
Stat Probab Lett
2013;
83
:1083-1093. [PMID:
23482421
PMCID:
PMC3587760
DOI:
10.1016/j.spl.2013.01.001
]
[
Citation(s) in
RCA
: 17
]
[
Impact Index Per Article: 1.5
]
[
Reference Citation Analysis
]
[
Abstract
]
[
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]
[
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]
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[Indexed: 12/01/2022]
Abstract
Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion.
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Key Words
Fractional Brownian motion
Hausdorff dimension
Lévy process
continuous time random walk
packing dimension
self-similarity
strictly stable process
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MESH Headings
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Grants
R01 EB012079 NIBIB NIH HHS
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Affiliation(s)
Mark M. Meerschaert
Department of Probability and Statistics, Michigan State University, East Lansing, MI 48824,
URL:
http://www.stt.msu.edu/users/mcubed/
Erkan Nane
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849,
URL:
http://www.auburn.edu/~ezn0001
Yimin Xiao
Department Statistics and Probability, Michigan State University, East Lansing, MI 48824,
URL:
http://www.stt.msu.edu/users/xiaoyimi
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12
Buckley S
. Anomalous heat kernel behaviour for the dynamic random conductance model.
ELECTRONIC COMMUNICATIONS IN PROBABILITY
2013. [DOI:
10.1214/ecp.v18-2525
]
[
Citation(s) in
RCA
: 1
]
[
Impact Index Per Article: 0.1
]
[
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]
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[Indexed: 11/19/2022]
Abstract
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Affiliation(s)
Stephen Buckley
University of Oxford
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13
Xiao Y
, Zheng X. Discrete fractal dimensions of the ranges of random walks in $${{\mathbb Z}^d}$$ associate with random conductances.
Probab Theory Relat Fields
2012. [DOI:
10.1007/s00440-012-0418-3
]
[
Citation(s) in
RCA
: 1
]
[
Impact Index Per Article: 0.1
]
[
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]
[
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]
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[Indexed: 11/29/2022]
Abstract
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14
König W
, Salvi M, Wolff T. Large deviations for the local times of a random walk among random conductances.
ELECTRONIC COMMUNICATIONS IN PROBABILITY
2012. [DOI:
10.1214/ecp.v17-1820
]
[
Citation(s) in
RCA
: 10
]
[
Impact Index Per Article: 0.8
]
[
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]
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[Indexed: 11/19/2022]
Abstract
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Affiliation(s)
Wolfgang König
WIAS and TU Berlin
Michele Salvi
TU Berlin
Tilman Wolff
WIAS Berlin
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15
Mourrat JC
. Scaling limit of the random walk among random traps on ℤd.
ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES
2011. [DOI:
10.1214/10-aihp387
]
[
Citation(s) in
RCA
: 8
]
[
Impact Index Per Article: 0.6
]
[
Reference Citation Analysis
]
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[Indexed: 11/19/2022]
Abstract
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16
Barlow MT
, Černý J. Erratum to: Convergence to fractional kinetics for random walks associated with unbounded conductances.
Probab Theory Relat Fields
2011. [DOI:
10.1007/s00440-011-0344-9
]
[
Citation(s) in
RCA
: 0
]
[
Impact Index Per Article: 0
]
[
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]
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[Indexed: 10/18/2022]
Abstract
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17
Biskup M
. Recent progress on the Random Conductance Model.
PROBABILITY SURVEYS
2011. [DOI:
10.1214/11-ps190
]
[
Citation(s) in
RCA
: 99
]
[
Impact Index Per Article: 7.6
]
[
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[Indexed: 11/19/2022]
Abstract
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18
Barlow MT
, Zheng X. The random conductance model with Cauchy tails.
ANN APPL PROBAB
2010. [DOI:
10.1214/09-aap638
]
[
Citation(s) in
RCA
: 6
]
[
Impact Index Per Article: 0.4
]
[
Reference Citation Analysis
]
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[Indexed: 11/19/2022]
Abstract
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19
Barlow MT
, Deuschel JD. Invariance principle for the random conductance model with unbounded conductances.
ANN PROBAB
2010. [DOI:
10.1214/09-aop481
]
[
Citation(s) in
RCA
: 63
]
[
Impact Index Per Article: 4.5
]
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Reference Citation Analysis
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[Indexed: 11/19/2022]
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