200 research outputs found
Regeneration in One-Dimensional Gibbs States and Chains with Complete Connections
Regeneration in One-Dimensional Gibbs States and Chains with Complete Connections
Local geometry of random geodesics on negatively curved surfaces
It is shown that the tessellation of a compact, negatively curved surface
induced by a typical long geodesic segment, when properly scaled, looks locally
like a Poisson line process. This implies that the global statistics of the
tessellation -- for instance, the fraction of triangles -- approach those of
the limiting Poisson line process.Comment: This version extends the results of the previous version to surfaces
with possibly variable negative curvatur
A control problem arising in the sequential design of experiments
The Pele problem. Starting from an initial point x not in his playing field, a football player is to dribble onto the field. Due to irregularities in the surface on which the player is dribbling, and perhaps also to small inconsistencies in his kick, the movement of the ball has a “random” component; moreover, a kick with the left foot tends to have a somewhat different effect than a kick with the right foot. The player’s objective is to move the ball onto the playing field with as few kicks as possible
Billiards in a general domain with random reflections
We study stochastic billiards on general tables: a particle moves according
to its constant velocity inside some domain until it hits the boundary and bounces randomly inside according to some
reflection law. We assume that the boundary of the domain is locally Lipschitz
and almost everywhere continuously differentiable. The angle of the outgoing
velocity with the inner normal vector has a specified, absolutely continuous
density. We construct the discrete time and the continuous time processes
recording the sequence of hitting points on the boundary and the pair
location/velocity. We mainly focus on the case of bounded domains. Then, we
prove exponential ergodicity of these two Markov processes, we study their
invariant distribution and their normal (Gaussian) fluctuations. Of particular
interest is the case of the cosine reflection law: the stationary distributions
for the two processes are uniform in this case, the discrete time chain is
reversible though the continuous time process is quasi-reversible. Also in this
case, we give a natural construction of a chord "picked at random" in
, and we study the angle of intersection of the process with a
-dimensional manifold contained in .Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics
and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains
Cellular homologs of the avian erythroblastosis virus erb-A and erb-B genes are syntenic in mouse but asyntenic in man.
Phase Transitions on Nonamenable Graphs
We survey known results about phase transitions in various models of
statistical physics when the underlying space is a nonamenable graph. Most
attention is devoted to transitive graphs and trees
Multifractal tubes
Tube formulas refer to the study of volumes of neighbourhoods of sets.
For sets satisfying some (possible very weak) convexity conditions, this has a
long history. However, within the past 20 years Lapidus has initiated and
pioneered a systematic study of tube formulas for fractal sets. Following this,
it is natural to ask to what extend it is possible to develop a theory of
multifractal tube formulas for multifractal measures. In this paper we propose
and develop a framework for such a theory. Firstly, we define multifractal tube
formulas and, more generally, multifractal tube measures for general
multifractal measures. Secondly, we introduce and develop two approaches for
analysing these concepts for self-similar multifractal measures, namely:
(1) Multifractal tubes of self-similar measures and renewal theory. Using
techniques from renewal theory we give a complete description of the asymptotic
behaviour of the multifractal tube formulas and tube measures of self-similar
measures satisfying the Open Set Condition.
(2) Multifractal tubes of self-similar measures and zeta-functions.
Unfortunately, renewal theory techniques do not yield "explicit" expressions
for the functions describing the asymptotic behaviour of the multifractal tube
formulas and tube measures of self-similar measures. This is clearly
undesirable. For this reason, we introduce and develop a second framework for
studying multifractal tube formulas of self-similar measures. This approach is
based on multifractal zeta-functions and allow us obtain "explicit" expressions
for the multifractal tube formulas of self-similar measures, namely, using the
Mellin transform and the residue theorem, we are able to express the
multifractal tube formulas as sums involving the residues of the zeta-function.Comment: 122 page
Mouse UDP-GlcNAc: dolichyl-phosphate N-acetylglucosaminephosphotransferase. Molecular cloning of the cDNA, generation of anti-peptide antibodies and chromosomal localization
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