Tail estimates for homogenization theorems in random media
ESAIM: Probability and Statistics (2009)
- Volume: 13, page 51-69
- ISSN: 1292-8100
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topBoivin, Daniel. "Tail estimates for homogenization theorems in random media." ESAIM: Probability and Statistics 13 (2009): 51-69. <http://eudml.org/doc/250668>.
@article{Boivin2009,
abstract = {
Consider a random environment in $\{\mathbb Z\}^d$ given by i.i.d. conductances.
In this work, we obtain tail estimates for the fluctuations about the
mean for the following characteristics of the environment:
the effective conductance between opposite faces of a cube,
the diffusion matrices of periodized environments
and the spectral gap of the random walk in a finite cube.
},
author = {Boivin, Daniel},
journal = {ESAIM: Probability and Statistics},
keywords = {Periodic approximation; random environments;
fluctuations; effective diffusion matrix; effective conductance;
non-uniform ellipticity; non-uniform ellipticity},
language = {eng},
month = {2},
pages = {51-69},
publisher = {EDP Sciences},
title = {Tail estimates for homogenization theorems in random media},
url = {http://eudml.org/doc/250668},
volume = {13},
year = {2009},
}
TY - JOUR
AU - Boivin, Daniel
TI - Tail estimates for homogenization theorems in random media
JO - ESAIM: Probability and Statistics
DA - 2009/2//
PB - EDP Sciences
VL - 13
SP - 51
EP - 69
AB -
Consider a random environment in ${\mathbb Z}^d$ given by i.i.d. conductances.
In this work, we obtain tail estimates for the fluctuations about the
mean for the following characteristics of the environment:
the effective conductance between opposite faces of a cube,
the diffusion matrices of periodized environments
and the spectral gap of the random walk in a finite cube.
LA - eng
KW - Periodic approximation; random environments;
fluctuations; effective diffusion matrix; effective conductance;
non-uniform ellipticity; non-uniform ellipticity
UR - http://eudml.org/doc/250668
ER -
References
top- I. Benjamini and R. Rossignol, Submean variance bound for effective resistance on random electric networks.v4 [math.PR] URIarXiv:math/0610393
- D. Boivin and J. Depauw, Spectral homogenization of reversible random walks on in a random environment. Stochastic Process. Appl.104 (2003) 29–56.
- D. Boivin and Y. Derriennic, The ergodic theorem for additive cocycles of or . Ergodic Theory Dynam. Syst.11 (1991) 19–39.
- E. Bolthausen and A.S. Sznitman, Ten lectures on random media. DMV Seminar, Band 32, Birkhäuser (2002).
- A. Bourgeat and A. Piatnitski, Approximations of effective coefficients in stochastic homogenization. Ann. Inst. H. Poincaré Probab. Statist.40 (2004) 153–165.
- P. Caputo and D. Ioffe, Finite volume approximation of the effective diffusion matrix: the case of independent bond disorder. Ann. Inst. H. Poincaré Probab. Statist.39 (2003) 505–525.
- F.R.K. Chung, Spectral graph theory. CBMS Regional Conference Series in Mathematics, 92. American Mathematical Society (1997).
- E.B. Davies, Heat kernels and spectral theory. Cambridge Tracts in Mathematics, 92. Cambridge University Press (1989).
- T. Delmotte, Inéalité de Harnack elliptique sur les graphes. Colloq. Math.72 (1997) 19–37.
- R. Durrett, Probability: Theory and Examples. Wadsworth & Brooks/Cole Statistics/Probability Series (1991).
- L.R.G. Fontes and P. Mathieu, On symmetric random walks with random conductances on . Probab. Theory Related Fields134 (2006) 565–602.
- T. Funaki and H. Spohn, Motion by mean curvature from the Ginzburg-Landau interface model. Commun. Math. Phys. 185 (1997) 1–36.
- G. Grimmett, Percolation. 2nd ed. Springer (1999).
- E. Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities. Courant Lecture Notes Mathematics 5. American Mathematical Society (2000).
- B.D. Hughes, Random walks and random environments. Vol. 2. Random environments. Oxford University Press (1996).
- V.V. Jikov, S.M. Kozlov and O.A. Olejnik, Homogenization of differential operators and integral functionals. Springer-Verlag (1994).
- S. Kesavan, Homogenization of elliptic eigenvalue problems I. Appl. Math. Optimization5 (1979) 153–167.
- H. Kesten, On the speed of convergence in first-passage percolation. Ann. Appl. Probab.3 (1993) 296–338.
- C. Kipnis and S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys.10 (1986) 1–19.
- S.M. Kozlov, The method of averaging and walks in inhomogeneous environments. Russ. Math. Surv.40 (1985) 73–145.
- R. Kuennemann, The diffusion limit for reversible jump processes on with ergodic random bond conductivities. Commun. Math. Phys.90 (1983) 27–68.
- H. Owhadi, Approximation of the effective conductivity of ergodic media by periodization. Probab. Theory Related Fields125 (2003) 225-258.
- E. Pardoux and A.Yu. Veretennikov, On the Poisson equation and diffusion approximation. I. Ann. Probab.29 (2001) 1061–1085.
- Y. Peres, Probability on trees: An introductory climb. Lectures on probability theory and statistics. École d'été de Probabilités de Saint-Flour XXVII-1997, Springer. Lect. Notes Math. 1717 (1999) 193–280 .
- L. Saloff-Coste, Lectures on finite Markov chains. Lectures on probability theory and statistics. École d'été de probabilités de Saint-Flour XXVI–1996, Springer. Lect. Notes Math. 1665 (1997) 301–413.
- V. Sidoravicius and A.-S. Sznitman, Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields129 (2004) 219–244.
- F. Spitzer, Principles of random walk. The University Series in Higher Mathematics. D. Van Nostrand Company (1964).
- J. Wehr, A lower bound on the variance of conductance in random resistor networks. J. Statist. Phys.86 (1997) 1359–1365.
- V.V. Yurinsky, Averaging of symmetric diffusion in random medium. Sib. Math. J.2 (1986) 603–613.
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