3,009 research outputs found
Conservation of geometric structures for non-homogeneous inviscid incompressible fluids
We obtain a result about propagation of geometric properties for solutions of
the non-homogeneous incompressible Euler system in any dimension . In
particular, we investigate conservation of striated and conormal regularity,
which is a natural way of generalizing the 2-D structure of vortex patches. The
results we get are only local in time, even in the dimension N=2; however, we
provide an explicit lower bound for the lifespan of the solution. In the case
of physical dimension N=2 or 3, we investigate also propagation of H\"older
regularity in the interior of a bounded domain
Holomorphic self-maps of singular rational surfaces
We give a new proof of the classification of normal singular surface germs
admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw
an analogy between the birational classification of singular holomorphic
foliations on surfaces, and the dynamics of holomorphic maps. Following this
analogy, we introduce the notion of minimal holomorphic model for holomorphic
maps. We give sufficient conditions which ensure the uniqueness of such a
model.Comment: 37 pages. To appear in Publicacions Matematiques
Convergence in law in the second Wiener/Wigner chaos
Let L be the class of limiting laws associated with sequences in the second
Wiener chaos. We exhibit a large subset L_0 of L satisfying that, for any
F_infinity in L_0, the convergence of only a finite number of cumulants
suffices to imply the convergence in law of any sequence in the second Wiener
chaos to F_infinity. This result is in the spirit of the seminal paper by
Nualart and Peccati, in which the authors discovered the surprising fact that
convergence in law for sequences of multiple Wiener-It\^o integrals to the
Gaussian is equivalent to convergence of just the fourth cumulant. Also, we
offer analogues of this result in the case of free Brownian motion and double
Wigner integrals, in the context of free probability.Comment: 14 pages. This version corrects an error which, unfortunately,
appears in the published version in EC
Sharp adaptive estimation of the drift function for ergodic diffusions
The global estimation problem of the drift function is considered for a large
class of ergodic diffusion processes. The unknown drift is supposed
to belong to a nonparametric class of smooth functions of order , but
the value of is not known to the statistician. A fully data-driven
procedure of estimating the drift function is proposed, using the estimated
risk minimization method. The sharp adaptivity of this procedure is proven up
to an optimal constant, when the quality of the estimation is measured by the
integrated squared error weighted by the square of the invariant density.Comment: Published at http://dx.doi.org/10.1214/009053605000000615 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On convergence-sensitive bisimulation and the embedding of CCS in timed CCS
We propose a notion of convergence-sensitive bisimulation that is built just
over the notions of (internal) reduction and of (static) context. In the
framework of timed CCS, we characterise this notion of `contextual'
bisimulation via the usual labelled transition system. We also remark that it
provides a suitable semantic framework for a fully abstract embedding of
untimed processes into timed ones. Finally, we show that the notion can be
refined to include sensitivity to divergence
Processes with Long Memory: Regenerative Construction and Perfect Simulation
We present a perfect simulation algorithm for stationary processes indexed by
Z, with summable memory decay. Depending on the decay, we construct the process
on finite or semi-infinite intervals, explicitly from an i.i.d. uniform
sequence. Even though the process has infinite memory, its value at time 0
depends only on a finite, but random, number of these uniform variables. The
algorithm is based on a recent regenerative construction of these measures by
Ferrari, Maass, Mart{\'\i}nez and Ney. As applications, we discuss the perfect
simulation of binary autoregressions and Markov chains on the unit interval.Comment: 27 pages, one figure. Version accepted by Annals of Applied
Probability. Small changes with respect to version
A continuum-tree-valued Markov process
We present a construction of a L\'evy continuum random tree (CRT) associated
with a super-critical continuous state branching process using the so-called
exploration process and a Girsanov's theorem. We also extend the pruning
procedure to this super-critical case. Let be a critical branching
mechanism. We set . Let
or be the set
of values of for which is a branching mechanism. The
pruning procedure allows to construct a decreasing L\'evy-CRT-valued Markov
process (\ct_\theta,\theta\in\Theta), such that has
branching mechanism . It is sub-critical if and
super-critical if . We then consider the explosion time of the
CRT: the smaller (negative) time for which has
finite mass. We describe the law of as well as the distribution of the CRT
just after this explosion time. The CRT just after explosion can be seen as a
CRT conditioned not to be extinct which is pruned with an independent intensity
related to . We also study the evolution of the CRT-valued process after the
explosion time. This extends results from Aldous and Pitman on Galton-Watson
trees. For the particular case of the quadratic branching mechanism, we show
that after explosion the total mass of the CRT behaves like the inverse of a
stable subordinator with index 1/2. This result is related to the size of the
tagged fragment for the fragmentation of Aldous' CRT
Haldane's Fractional Statistics and the Riemann-Roch Theorem
The new definition of fractional statistics given by Haldane can be
understood in some special cases in terms of the Riemann-Roch theorem.Comment: 38050 Povo, Trento and Division de Physique Th\'eorique, IPN, 91406
Orsay Cedex, 19 pages, IPNO/TH 94-11, SISSA/27/94/EP,UFT/32
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