1,844 research outputs found
Feller property and infinitesimal generator of the exploration process
We consider the exploration process associated to the continuous random tree
(CRT) built using a Levy process with no negative jumps. This process has been
studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is
a useful tool to study CRT as well as super-Brownian motion with general
branching mechanism. In this paper we prove this process is Feller, and we
compute its infinitesimal generator on exponential functionals and give the
corresponding martingale
Orbital frustration at the origin of the magnetic behavior in LiNiO2
We report on the ESR, magnetization and magnetic susceptibility measurements
performed over a large temperature range, from 1.5 to 750 K, on high-quality
stoichiometric LiNiO2. We find that this compound displays two distinct
temperature regions where its magnetic behavior is anomalous. With the help of
a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that
below T_of ~ 400 K, an orbitally-frustrated state characteristic of the
triangular lattice is established. This then gives a solution to the
long-standing controversial problem of the magnetic behavior in LiNiO2.Comment: 5 pages, 5 figures, RevTex, accepted in PR
Bessel processes, the Brownian snake and super-Brownian motion
We prove that, both for the Brownian snake and for super-Brownian motion in
dimension one, the historical path corresponding to the minimal spatial
position is a Bessel process of dimension -5. We also discuss a spine
decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in
memory of Marc Yo
Salto de Truel
En este salto sobre el rio Tarn (Francia) se aprovechan las aguas del rio con un desnivel comprendido entre el del remanso del salto de La Jourdanie (situado aguas abajo) y el nivel de restitución de aguas del salto de Pinet (emplazado aguas arriba)
Random trees between two walls: Exact partition function
We derive the exact partition function for a discrete model of random trees
embedded in a one-dimensional space. These trees have vertices labeled by
integers representing their position in the target space, with the SOS
constraint that adjacent vertices have labels differing by +1 or -1. A
non-trivial partition function is obtained whenever the target space is bounded
by walls. We concentrate on the two cases where the target space is (i) the
half-line bounded by a wall at the origin or (ii) a segment bounded by two
walls at a finite distance. The general solution has a soliton-like structure
involving elliptic functions. We derive the corresponding continuum scaling
limit which takes the remarkable form of the Weierstrass p-function with
constrained periods. These results are used to analyze the probability for an
evolving population spreading in one dimension to attain the boundary of a
given domain with the geometry of the target (i) or (ii). They also translate,
via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main
modifications in Sect. 5-6 and conclusio
Confluence of geodesic paths and separating loops in large planar quadrangulations
We consider planar quadrangulations with three marked vertices and discuss
the geometry of triangles made of three geodesic paths joining them. We also
study the geometry of minimal separating loops, i.e. paths of minimal length
among all closed paths passing by one of the three vertices and separating the
two others in the quadrangulation. We concentrate on the universal scaling
limit of large quadrangulations, also known as the Brownian map, where pairs of
geodesic paths or minimal separating loops have common parts of non-zero
macroscopic length. This is the phenomenon of confluence, which distinguishes
the geometry of random quadrangulations from that of smooth surfaces. We
characterize the universal probability distribution for the lengths of these
common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding
paragraph and one reference added, and several other small correction
Searching for Stable Na-ordered Phases in Single Crystal Samples of gamma-NaxCoO2
We report on the preparation and characterization of single crystal gamma
phase NaxCoO2 with 0.25 < x < 0.84 using a non-aqueous electrochemical
chronoamperemetry technique. By carefully mapping the overpotential versus x
(for x < 0.84), we find six distinct stable phases with Na levels corresponding
to x ~ 0.75, 0.71, 0.50, 0.43, 0.33 and 0.25. The composition with x ~0.55
appears to have a critical Na concentration which separates samples with
different magnetic behavior as well as different Na ion diffusion mechanisms.
Chemical analysis of an aged crystal reveals different Na ion diffusion
mechanisms above and below x_c ~ 0.53, where the diffusion process above x_c
has a diffusion coefficient about five times larger than that below x_c. The
series of crystals were studied with X-ray diffraction, susceptibility, and
transport measurements. The crystal with x = 0.5 shows a weak ferromagnetic
transition below T=27 K in addition to the usual transitions at T = 51 K and 88
K. The resistivity of the Curie-Weiss metallic Na0.71CoO2 composition has a
very low residual resistivity, which attests to the high homogeneity of the
crystals prepared by this improved electrochemical method. Our results on the
various stable crystal compositions point to the importance of Na ion ordering
across the phase diagram.Comment: 9 pages, 9 figure
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