367 research outputs found
Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
Brownian Motion in wedges, last passage time and the second arc-sine law
We consider a planar Brownian motion starting from at time and
stopped at and a set of semi-infinite
straight lines emanating from . Denoting by the last time when is
reached by the Brownian motion, we compute the probability law of . In
particular, we show that, for a symmetric and even values, this law can
be expressed as a sum of or functions. The original
result of Levy is recovered as the special case . A relation with the
problem of reaction-diffusion of a set of three particles in one dimension is
discussed
Rainfall estimation in the Sahel : the EPSAT-NIGER experiment
Le projet EPSAT-Niger (Estimation des Précipitations par Satellite-expérience Niger) est une expérience destinée à améliorer notre connaissance des systèmes précipitants de l'Afrique soudano-sahélienne, et à mettre au point des algorithmes opérationnels d'estimation des pluies sur cette région. Elle s'appuie sur l'utilisation conjointe d'un réseau de pluviographes (93 postes sur 16.000 km2) et d'un radar météorologique bande C. Sa durée prévue est de trois ans (1990-1992). La géométrie du réseau, une grille régulière dont la maille mesure 12.5 km de côté, dotée d'une cible où la distance entre postes descend à 1 km, a permis de mener à bien des études préliminaires sur la répartition des pluies à différentes échelles de temps et d'espace. Le gradient pluviométrique Sud-Nord des moyennes interannuelles est fortement altéré quand on travaille sur une saison particulière. La variabilité locale des cumuls saisonniers peut être extrêmement importante. Des écarts de 60 % sur moins de 10 km ont été enregistrés. L'exploitation conjointe des données sol et radar conduit à mettre en évidence certaines particularités des lignes de grains et s'avère prometteuse pour mettre au point une vérité sol adaptée à la validation des données satellitaires. (Résumé d'auteur
Random Operator Approach for Word Enumeration in Braid Groups
We investigate analytically the problem of enumeration of nonequivalent
primitive words in the braid group B_n for n >> 1 by analysing the random word
statistics and the target space on the basis of the locally free group
approximation. We develop a "symbolic dynamics" method for exact word
enumeration in locally free groups and bring arguments in support of the
conjecture that the number of very long primitive words in the braid group is
not sensitive to the precise local commutation relations. We consider the
connection of these problems with the conventional random operator theory,
localization phenomena and statistics of systems with quenched disorder. Also
we discuss the relation of the particular problems of random operator theory to
the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl.
Phys. B [PM
Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant
We consider a particle diffusing along the links of a general graph
possessing some absorbing vertices. The particle, with a spatially-dependent
diffusion constant D(x) is subjected to a drift U(x) that is defined in every
point of each link. We establish the boundary conditions to be used at the
vertices and we derive general expressions for the average time spent on a part
of the graph before absorption and, also, for the Laplace transform of the
joint law of the occupation times. Exit times distributions and splitting
probabilities are also studied and several examples are discussed.Comment: Accepted for publication in J. Phys.
Finite pseudo orbit expansions for spectral quantities of quantum graphs
We investigate spectral quantities of quantum graphs by expanding them as
sums over pseudo orbits, sets of periodic orbits. Only a finite collection of
pseudo orbits which are irreducible and where the total number of bonds is less
than or equal to the number of bonds of the graph appear, analogous to a cut
off at half the Heisenberg time. The calculation simplifies previous approaches
to pseudo orbit expansions on graphs. We formulate coefficients of the
characteristic polynomial and derive a secular equation in terms of the
irreducible pseudo orbits. From the secular equation, whose roots provide the
graph spectrum, the zeta function is derived using the argument principle. The
spectral zeta function enables quantities, such as the spectral determinant and
vacuum energy, to be obtained directly as finite expansions over the set of
short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy
calculation expande
Heated nuclear matter, condensation phenomena and the hadronic equation of state
The thermodynamic properties of heated nuclear matter are explored using an
exactly solvable canonical ensemble model. This model reduces to the results of
an ideal Fermi gas at low temperatures. At higher temperatures, the
fragmentation of the nuclear matter into clusters of nucleons leads to features
that resemble a Bose gas. Some parallels of this model with the phenomena of
Bose condensation and with percolation phenomena are discussed. A simple
expression for the hadronic equation of state is obtained from the model.Comment: 12 pages, revtex, 1 ps file appended (figure 1
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
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