637 research outputs found
Quenched central limit theorem for the stochastic heat equation in weak disorder
We continue with the study of the mollified stochastic heat equation in
given by with spatially
smoothened cylindrical Wiener process , whose (renormalized) Feynman-Kac
solution describes the partition function of the continuous directed polymer.
In an earlier work (\cite{MSZ16}), a phase transition was obtained, depending
on the value of in the limiting object of the smoothened solution
as the smoothing parameter This partition function
naturally defines a quenched polymer path measure and we prove that as long as
stays small enough while converges to a strictly
positive non-degenerate random variable, the distribution of the diffusively
rescaled Brownian path converges under the aforementioned polymer path measure
to standard Gaussian distribution.Comment: Minor revisio
The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature
We study a spin system on a large box with both Ising interaction and
Sherrington-Kirpatrick couplings, in the presence of an external field. Our
results are: (i) existence of the pressure in the limit of an infinite box.
When both Ising and Sherrington-Kirpatrick temperatures are high enough, we
prove that: (ii) the value of the pressure is given by a suitable replica
symmetric solution, and (iii) the fluctuations of the pressure are of order of
the inverse of the square of the volume with a normal distribution in the
limit. In this regime, the pressure can be expressed in terms of random field
Ising models
Quenched invariance principle for the Knudsen stochastic billiard in a random tube
We consider a stochastic billiard in a random tube which stretches to
infinity in the direction of the first coordinate. This random tube is
stationary and ergodic, and also it is supposed to be in some sense well
behaved. The stochastic billiard can be described as follows: when strictly
inside the tube, the particle moves straight with constant speed. Upon hitting
the boundary, it is reflected randomly, according to the cosine law: the
density of the outgoing direction is proportional to the cosine of the angle
between this direction and the normal vector. We also consider the
discrete-time random walk formed by the particle's positions at the moments of
hitting the boundary. Under the condition of existence of the second moment of
the projected jump length with respect to the stationary measure for the
environment seen from the particle, we prove the quenched invariance principles
for the projected trajectories of the random walk and the stochastic billiard.Comment: Published in at http://dx.doi.org/10.1214/09-AOP504 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Stretched Polymers in Random Environment
We survey recent results and open questions on the ballistic phase of
stretched polymers in both annealed and quenched random environments.Comment: Dedicated to Erwin Bolthausen on the occasion of his 65th birthda
Knudsen gas in a finite random tube: transport diffusion and first passage properties
We consider transport diffusion in a stochastic billiard in a random tube
which is elongated in the direction of the first coordinate (the tube axis).
Inside the random tube, which is stationary and ergodic, non-interacting
particles move straight with constant speed. Upon hitting the tube walls, they
are reflected randomly, according to the cosine law: the density of the
outgoing direction is proportional to the cosine of the angle between this
direction and the normal vector. Steady state transport is studied by
introducing an open tube segment as follows: We cut out a large finite segment
of the tube with segment boundaries perpendicular to the tube axis. Particles
which leave this piece through the segment boundaries disappear from the
system. Through stationary injection of particles at one boundary of the
segment a steady state with non-vanishing stationary particle current is
maintained. We prove (i) that in the thermodynamic limit of an infinite open
piece the coarse-grained density profile inside the segment is linear, and (ii)
that the transport diffusion coefficient obtained from the ratio of stationary
current and effective boundary density gradient equals the diffusion
coefficient of a tagged particle in an infinite tube. Thus we prove Fick's law
and equality of transport diffusion and self-diffusion coefficients for quite
generic rough (random) tubes. We also study some properties of the crossing
time and compute the Milne extrapolation length in dependence on the shape of
the random tube.Comment: 51 pages, 3 figure
Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher
We consider large deviations for nearest-neighbor random walk in a uniformly
elliptic i.i.d. environment. It is easy to see that the quenched and the
averaged rate functions are not identically equal. When the dimension is at
least four and Sznitman's transience condition (T) is satisfied, we prove that
these rate functions are finite and equal on a closed set whose interior
contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title
of the paper. To appear in Probability Theory and Related Fields
Possible Indication of Narrow Baryonic Resonances Produced in the 1720-1790 MeV Mass Region
Signals of two narrow structures at M=1747 MeV and 1772 MeV were observed in
the invariant masses M_{pX} and M_{\pi^{+}X} of the pp->ppX and pp->p\pi^{+}X
reactions respectively. Many tests were made to see if these structures could
have been produced by experimental artefacts. Their small widths and the
stability of the extracted masses lead us to conclude that these structures are
genuine and may correspond to new exotic baryons. Several attempts to identify
them, including the possible "missing baryons" approach, are discussed.Comment: 17 pages including 8 figures and 3 tables. ReVte
The Continuum Directed Random Polymer
Motivated by discrete directed polymers in one space and one time dimension,
we construct a continuum directed random polymer that is modeled by a
continuous path interacting with a space-time white noise. The strength of the
interaction is determined by an inverse temperature parameter beta, and for a
given beta and realization of the noise the path evolves in a Markovian way.
The transition probabilities are determined by solutions to the one-dimensional
stochastic heat equation. We show that for all beta > 0 and for almost all
realizations of the white noise the path measure has the same Holder continuity
and quadratic variation properties as Brownian motion, but that it is actually
singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page
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