Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics

By Antoine Gloria, Stefan Neukamm, Felix Otto. 2013

280 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6147fb52dbe8db6e09c4758b49d9bf46cfd0a113

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form (2013, background): “In recent and striking papers, Gloria and Otto [10] and Gloria, Neukamm and Otto [9] proved optimal error estimates for discrete elliptic equations in divergence form with i.i.d. coefficients, using a combination of regularity theory and concentration arguments.”
Quantitative Stochastic Homogenization and Large-Scale Regularity (2017, background): “1, but with much weaker stochastic integrability, were proved several years earlier in [65, 66, 62, 67] for a certain class of random environments”
Lipschitz Regularity for Elliptic Equations with Random Coefficients (2014, methodology): “Expounding on this work and some ideas developed independently in [32], these authors and Neukamm [22,23] then proved optimal estimates and a quantitative two-scale expansion for uniformly elliptic equations under quantitative assumptions built on spectral gap-type concentration inequalities.”
A Regularity Theory for Random Elliptic Operators (2014, methodology): “In contrast to our framework based on nonlinear mixing conditions (as developed in [41, 43, 38] and the present paper), Armstrong and Smart quantify ergodicity in terms of linear mixing conditions.”
The additive structure of elliptic homogenization (2016, methodology): “Before the regularity theory was introduced in [4], the best estimates available (see [16, 28]) were finite moment bounds.”
Quantitative results on the corrector equation in stochastic homogenization (2014, methodology): “15) In the discrete setting we proved in [13], using a semi-group approach, that 〈dG(dλ)d〉 ([0, ν]) .”
Quantitative stochastic homogenization and regularity theory of parabolic equations (2017, background): “This essentially began with the work of Gloria and Otto [19, 20], who proved the first quantitative results which are optimal in the scaling of the parameter ε (see also [18]).”
Mesoscopic Higher Regularity and Subadditivity in Elliptic Homogenization (2015, background): “A similar result was recently proved by Fischer and Otto [9], who developed a similar higher regularity theory in the general stationary ergodic setting.”
Quantitative estimates in stochastic homogenization for correlated coefficient fields (2019, methodology): “The combination of these three ingredients resulted in [19], where we proved optimal estimates in any dimension for scalar equations under a quantified ergodicity assumption in the form of a spectral gap estimate.”