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Random Matrices and Complexity of Spin Glasses

- Antonio Auffinger, G. B. Arous, J. Černý
- Computer Science
- 4 March 2010

TLDR

The arcsine law as a universal aging scheme for trap models

- G. B. Arous, J. Černý
- Computer Science, Mathematics
- 14 March 2006

We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the… Expand

Convergence to fractional kinetics for random walks associated with unbounded conductances

We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics… Expand

Aging in two-dimensional Bouchaud's model

- G. Ben Arous, J. Černý, T. Mountford
- Mathematics
- 2006

Let Ex be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by wxy = ν exp (−βEx) if x, y are neighbours in… Expand

Directed random walk on the backbone of an oriented percolation cluster

- M. Birkner, J. Černý, A. Depperschmidt, N. Gantert
- Mathematics
- 13 April 2012

We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the "ancestral lineage'' of an… Expand

Dynamics of trap models

- G. B. Arous, J. Černý
- Geology
- 14 March 2006

These notes cover one of the topics of the class given in the Les Houches Summer School ``Mathematical statistical physics'' in July 2005. The lectures tried to give a summary of the recent… Expand

Moments and distribution of the local time of a two-dimensional random walk

- J. Černý
- Mathematics
- 1 February 2007

GIANT VACANT COMPONENT LEFT BY A RANDOM WALK IN A RANDOM d-REGULAR GRAPH

- J. Černý, A. Teixeira, David Windisch
- Mathematics
- 22 December 2010

We study the trajectory of a simple random walk on a d-regular graph with d � 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular… Expand

Bouchaud’s model exhibits two different aging regimes in dimension one

- G. B. Arous, J. Černý
- Mathematics
- 29 October 2002

Let E_i be a collection of i.i.d. exponential random variables. Bouchaud's model on Z is a Markov chain X(t) whose transition rates are given by w_{ij}=\nu \exp(-\beta ((1-a)E_i-aE_j)) if i, j are… Expand

On Two-Dimensional Random Walk Among Heavy-Tailed Conductances

- J. Černý
- Mathematics
- 2 June 2011

We consider a random walk among unbounded random conductances on the two-dimensional integer lattice. When the distribution of the conductances has an infinite expectation and a polynomial tail, we… Expand

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