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 …
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 …
of surprising phenomena and challenging problems, especially in the non-reversible …
[KNIHA][B] Fluctuations in Markov processes: time symmetry and martingale approximation
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 …
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 …
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 …
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 …
such as fractals and percolation clusters by means of both probabilistic and analytic …
Convergence of uniform triangulations under the Cardy embedding
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 …
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 …
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 …
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 …
The Annals of Probability 2010, Vol. 38, No. 1, 234–276 DOI: 10.1214/09-AOP481 © Institute of …