Recent progress on the random conductance model

M Biskup - 2011 - projecteuclid.org
Recent progress on the understanding of the Random Conductance Model is reviewed and
commented. A particular emphasis is on the results on the scaling limit of the random walk …

Random walks in random environments

O Zeitouni - Journal of Physics A: Mathematical and General, 2006 - iopscience.iop.org
Random walks in random environments and their diffusion analogues have been a source
of surprising phenomena and challenging problems, especially in the non-reversible …

[KNIHA][B] Fluctuations in Markov processes: time symmetry and martingale approximation

T Komorowski, C Landim, S Olla - 2012 - books.google.com
The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

[KNIHA][B] Progress in high-dimensional percolation and random graphs

M Heydenreich, R Van der Hofstad - 2017 - Springer
This book focuses on percolation on high-dimensional lattices. We give a general
introduction to percolation, stating the main results and defining the central objects. We …

Quenched invariance principles for random walks on percolation clusters

P Mathieu, A Piatnitski - Proceedings of the Royal Society …, 2007 - royalsocietypublishing.org
Quenched invariance principles for random walks on percolation clusters | Proceedings of the
Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …

[KNIHA][B] Random walks on disordered media and their scaling limits

T Kumagai - 2014 - Springer
The main theme of these lecture notes is to analyze heat conduction on disordered media
such as fractals and percolation clusters by means of both probabilistic and analytic …

Convergence of uniform triangulations under the Cardy embedding

N Holden, X Sun - arxiv preprint arxiv:1905.13207, 2019 - arxiv.org
We consider an embedding of planar maps into an equilateral triangle $\Delta $ which we
call the Cardy embedding. The embedding is a discrete approximation of a conformal map …

Quenched invariance principles for random walks with random conductances

P Mathieu - Journal of Statistical Physics, 2008 - Springer
Quenched Invariance Principles for Random Walks with Random Conductances Page 1 J Stat
Phys (2008) 130: 1025–1046 DOI 10.1007/s10955-007-9465-z Quenched Invariance Principles …

The Alexander-Orbach conjecture holds in high dimensions

G Kozma, A Nachmias - Inventiones mathematicae, 2009 - Springer
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-
field behavior has been established, namely when the dimension d is large enough or when …

Invariance principle for the random conductance model with unbounded conductances

MT Barlow, JD Deuschel - 2010 - projecteuclid.org
Invariance principle for the random conductance model with unbounded conductances Page 1
The Annals of Probability 2010, Vol. 38, No. 1, 234–276 DOI: 10.1214/09-AOP481 © Institute of …