55 citations · 87 across the 11 of their papers we have counts for
12 papers
Rigidity of harmonic functions on the supercritical percolation cluster
Ahmed Bou-Rabee, William Cooperman, Paul Dario
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a L…
Upper bounds on the fluctuations for a class of degenerate convex -interface models
Paul Dario
We derive upper bounds on the fluctuations of a class of random surfaces of the -type with convex interaction potentials. The Brascamp-Lieb concentration inequality provi…
Quantitative hydrodynamic limits of the Langevin dynamics for gradient interface models
Scott Armstrong, Paul Dario
We study the Langevin dynamics corresponding to the (or Ginzburg-Landau) interface model with a uniformly convex interaction potential. We interpret these Langevin dynami…
Convergence to the thermodynamic limit for random-field random surfaces
Paul Dario
We study random surfaces with a uniformly convex gradient interaction in the presence of quenched disorder taking the form of a random independent external field. Previous work on…
Random-field random surfaces
Paul Dario, Matan Harel, Ron Peled
We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The r…
Quantitative disorder effects in low-dimensional spin systems
Paul Dario, Matan Harel, Ron Peled
The Imry-Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin…
Massless Phases for the Villain model in
Paul Dario, Wei Wu
We consider the classical Villain rotator model in at sufficiently low temperature, and prove that the truncated two-point function decays asymptotically as…
Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters
Paul Dario, Chenlin Gu
We study the heat kernel and the Green's function on the infinite supercritical percolation cluster in dimension and prove a quantitative homogenization theorem for thes…
Quantitative homogenization of the disordered model
Paul Dario
We study the model with uniformly convex Hamiltonian and prove a quantitative rate of convergence for the finite-volume surface ten…
Quantitative Homogenization of Differential Forms
Paul Dario
We develop a quantitative theory of stochastic homogenization in the more general framework of differential forms. Inspired by recent progress in the uniformly elliptic setting, th…
Optimal corrector estimates on percolation clusters
Paul Dario
We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in and have logarithmic growth…
Elliptic regularity and quantitative homogenization on percolation clusters
Scott Armstrong, Paul Dario
We establish quantitative homogenization, large-scale regularity and Liouville results for the random conductance model on a supercritical (Bernoulli bond) percolation cluster. The…