52 citations · 247 across the 19 of their papers we have counts for
22 papers · 1 filter
Anchored Nash inequalities and heat kernel bounds for a class of random conductance models with long-range jumps
Sebastian Andres, Xin Chen, Martin Slowik +1
We show anchored versions of the Nash inequality for discrete non-local divergence-form operators with degenerate weights. They allow to control the -norm of a function by D…
Scaling limits for nonlinear functionals of the discrete Gaussian free field with degenerate random conductances
Christof F. Peter, Martin Slowik
We consider nonlinear functionals of discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of , including i.i.d. supercritic…
Invariance principles for rough walks in random conductances
Johannes Bäumler, Noam Berger, Tal Orenshtein +1
We establish annealed and quenched invariance principles for random walks in random conductances lifted to the p-variation rough path topology, allowing for degenerate environments…
Scaling limit of the discrete Gaussian free field with degenerate random conductances
Sebastian Andres, Martin Slowik, Anna-Lisa Sokol
We consider discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of , , including i.i.d.\ supercritical percolati…
Metastability for the Curie-Weiss-Potts model with unbounded random interactions
Johan L. A. Dubbeldam, Vicente Lenz Burnier, Elena Pulvirenti +1
We analyse the metastable behaviour of the disordered Curie--Weiss--Potts (DCWP) model subject to a Glauber dynamics. The model is a randomly disordered version of the mean-field $…
Quenched invariance principle for random walks in random environments admitting a cycle decomposition
Jean-Dominique Deuschel, Martin Slowik, Weile Weng
We study a class of non-reversible, continuous-time random walks in random environments on that admit a cycle representation with finite cycle length. The law of the…
Invariance principle and local limit theorem for a class of random conductance models with long-range jumps
Sebastian Andres, Martin Slowik
We study continuous time random walks on (with ) among random conductances that permit jumps of arbitrary length.…
Gradient estimates of the heat kernel for random walks among time-dependent random conductances
Jean-Dominique Deuschel, Takashi Kumagai, Martin Slowik
In this paper we consider a time-continuous random walk in in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these ra…
Metastability of Glauber dynamics with inhomogeneous coupling disorder
Anton Bovier, Frank den Hollander, Saeda Marello +2
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted…
A branching process model for dormancy and seed banks in randomly fluctuating environments
Jochen Blath, Felix Hermann, Martin Slowik
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (co…
Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights
Sebastian Andres, Alberto Chiarini, Martin Slowik
We establish a quenched local central limit theorem for the dynamic random conductance model on only assuming ergodicity with respect to space-time shifts and a mome…
Green kernel asymptotics for two-dimensional random walks under random conductances
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
We consider random walks among random conductances on and establish precise asymptotics for the associated potential kernel and the Green's function of the walk kill…
Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
We establish heat kernel upper bounds for a continuous-time random walk under unbounded conductances satisfying an integrability assumption, where we correct and extend recent resu…
Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities
André Schlichting, Martin Slowik
We investigate the metastable behavior of reversible Markov chains on possibly countable infinite state spaces. Based on a new definition of metastable Markov processes, we compute…
Homogenization theory for the random conductance model with degenerate ergodic weights and unbounded-range jumps
Franziska Flegel, Martin Heida, Martin Slowik
We study homogenization properties of the discrete Laplace operator with random conductances on a large domain in . More precisely, we prove almost-sure homogenizatio…
Invariance Principle for the one-dimensional dynamic Random Conductance Model under Moment Conditions
Jean-Dominique Deuschel, Martin Slowik
Recent progress in the understanding of quenched invariance principles (QIP) for a continuous-time random walk on in an environment of dynamical random conductances…
Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights
Jean-Dominique Deuschel, Tuan Anh Nguyen, Martin Slowik
We consider a stationary and ergodic random field that is parameterized by the edge set of the Euclidean lattice , . The random varia…
The enhanced Sanov theorem and propagation of chaos
Jean-Dominique Deuschel, Peter K. Friz, Mario Maurelli +1
We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (-layer, enhanced) empirical m…
Quenched invariance principle for random walks with time-dependent ergodic degenerate weights
Sebastian Andres, Alberto Chiarini, Jean-Dominique Deuschel +1
We study a continuous-time random walk, , on in an environment of dynamic random conductances taking values in . We assume that the law of the conduc…
Heat kernel estimates for random walks with degenerate weights
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
We establish Gaussian-type upper bounds on the heat kernel for a continuous-time random walk on a graph with unbounded weights under an ergodicity assumption. For the proof we use…
Harnack inequalities on weighted graphs and some applications to the random conductance model
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk in…
Invariance principle for the random conductance model in a degenerate ergodic environment
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
We study a continuous time random walk, , on in an environment of random conductances taking values in . We assume that the law of the conductances…