1,467 research outputs found
One Thousand and One Bubbles
We propose a novel strategy that permits the construction of completely
general five-dimensional microstate geometries on a Gibbons-Hawking space. Our
scheme is based on two steps. First, we rewrite the bubble equations as a
system of linear equations that can be easily solved. Second, we conjecture
that the presence or absence of closed timelike curves in the solution can be
detected through the evaluation of an algebraic relation. The construction we
propose is systematic and covers the whole space of parameters, so it can be
applied to find all five-dimensional BPS microstate geometries on a
Gibbons-Hawking base. As a first result of this approach, we find that the
spectrum of scaling solutions becomes much larger when non-Abelian fields are
present. We use our method to describe several smooth horizonless multicenter
solutions with the asymptotic charges of three-charge (Abelian and non-Abelian)
black holes. In particular, we describe solutions with the centers lying on
lines and circles that can be specified with exact precision. We show the power
of our method by explicitly constructing a 50-center solution. Moreover, we use
it to find the first smooth five-dimensional microstate geometries with
arbitrarily small angular momentum.Comment: 33 pages. v2: typos correcte
Fluctuations of the front in a stochastic combustion model
We consider an interacting particle system on the one dimensional lattice
modeling combustion. The process depends on two integer parameters
. Particles move independently as continuous time simple
symmetric random walks except that 1. When a particle jumps to a site which has
not been previously visited by any particle, it branches into particles; 2.
When a particle jumps to a site with particles, it is annihilated. We start
from a configuration where all sites to the left of the origin have been
previously visited and study the law of large numbers and central limit theorem
for , the rightmost visited site at time .
The proofs are based on the construction of a renewal structure leading to a
definition of regeneration times for which good tail estimates can be
performed.Comment: 19 page
Front propagation in an exclusion one-dimensional reactive dynamics
We consider an exclusion process representing a reactive dynamics of a pulled
front on the integer lattice, describing the dynamics of first class
particles moving as a simple symmetric exclusion process, and static second
class particles. When an particle jumps to a site with a particle,
their position is intechanged and the particle becomes an one.
Initially, there is an arbitrary configuration of particles at sites , and particles only at sites , with a product Bernoulli law
of parameter . We prove a law of large numbers and a central
limit theorem for the front defined by the right-most visited site of the
particles at time . These results corroborate Monte-Carlo simulations
performed in a similar context. We also prove that the law of the particles
as seen from the front converges to a unique invariant measure. The proofs use
regeneration times: we present a direct way to define them within this context.Comment: 19 page
Transition asymptotics for reaction-diffusion in random media
We describe a universal transition mechanism characterizing the passage to an
annealed behavior and to a regime where the fluctuations about this behavior
are Gaussian, for the long time asymptotics of the empirical average of the
expected value of the number of random walks which branch and annihilate on
, with stationary random rates. The random walks are
independent, continuous time rate , simple, symmetric, with . A random walk at , binary branches at rate ,
and annihilates at rate . The random environment has coordinates
which are i.i.d. We identify a natural way to describe
the annealed-Gaussian transition mechanism under mild conditions on the rates.
Indeed, we introduce the exponents
, and assume
that for
small enough, where and
denotes the average of the expected value of the number of particles
at time and an environment of rates , given that initially there was
only one particle at 0. Then the empirical average of over a box of
side has different behaviors: if for some and large enough , a law of large
numbers is satisfied; if for some
and large enough , a CLT is satisfied. These statements are
violated if the reversed inequalities are satisfied for some negative
. Applications to potentials with Weibull, Frechet and double
exponential tails are given.Comment: To appear in: Probability and Mathematical Physics: A Volume in Honor
of Stanislav Molchanov, Editors - AMS | CRM, (2007
Sharp ellipticity conditions for ballistic behavior of random walks in random environment
We sharpen the ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ramírez which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies the polynomial ballisticity criteria of Berger, Drewitz and Ramírez. As a corollary we can exhibit a new range of values for the parameters of Dirichlet random environments in dimension under which the corresponding random walk is ballistic
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