1,123 research outputs found
An elementary proof for the dimension of the graph of the classical Weierstrass function
Let where
is an integer and (classical Weierstrass
function). Building on work by Ledrappier (1992), Bar\'ansky, B\'ar\'any and
Romanowska (2013) and Tsujii (2001), we provide an elementary proof that the
Hausdorff dimension of equals
for all with a suitable . This
reproduces results by Bar\'ansky, B\'ar\'any and Romanowska without using the
dimension theory for hyperbolic measures of Ledrappier and Young (1985,1988),
which is replaced by a simple telescoping argument together with a recursive
multi-scale estimate.Comment: The proof of Proposition 3.3 is clarified and a mistake is correcte
Map Lattices coupled by collisions
We introduce a new coupled map lattice model in which the weak interaction
takes place via rare "collisions". By "collision" we mean a strong (possibly
discontinuous) change in the system. For such models we prove uniqueness of the
SRB measure and exponential space-time decay of correlations
Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling
We construct a mixing continuous piecewise linear map on [-1,1] with the
property that a two-dimensional lattice made of these maps with a linear north
and east nearest neighbour coupling admits a phase transition. We also provide
a modification of this construction where the local map is an expanding
analytic circle map. The basic strategy is borroughed from [Gielis-MacKay
(2000)], namely we compare the dynamics of the CML to those of a probabilistic
cellular automaton of Toom's type.Comment: 19 page
Random walk in Markovian environment
We prove a quenched central limit theorem for random walks with bounded
increments in a randomly evolving environment on . We assume that
the transition probabilities of the walk depend not too strongly on the
environment and that the evolution of the environment is Markovian with strong
spatial and temporal mixing properties.Comment: Published in at http://dx.doi.org/10.1214/07-AOP369 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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