918 research outputs found
Pattern theorems, ratio limit theorems and Gumbel maximal clusters for random fields
We study occurrences of patterns on clusters of size n in random fields on
Z^d. We prove that for a given pattern, there is a constant a>0 such that the
probability that this pattern occurs at most an times on a cluster of size n is
exponentially small. Moreover, for random fields obeying a certain Markov
property, we show that the ratio between the numbers of occurrences of two
distinct patterns on a cluster is concentrated around a constant value. This
leads to an elegant and simple proof of the ratio limit theorem for these
random fields, which states that the ratio of the probabilities that the
cluster of the origin has sizes n+1 and n converges as n tends to infinity.
Implications for the maximal cluster in a finite box are discussed.Comment: 23 pages, 2 figure
The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics
We consider the continuous time version of the Random Walk Pinning Model
(RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on
Z^d with jump rate rho (that plays the role of the random medium), we modify
the law of a random walk X on Z^d with jump rate 1 by reweighting the paths,
giving an energy reward proportional to the intersection time L_t(X,Y)=\int_0^t
\ind_{X_s=Y_s}\dd s: the weight of the path under the new measure is exp(beta
L_t(X,Y)), beta in R. As beta increases, the system exhibits a
delocalization/localization transition: there is a critical value beta_c, such
that if beta>beta_c the two walks stick together for almost-all Y realizations.
A natural question is that of disorder relevance, that is whether the quenched
and annealed systems have the same behavior. In this paper we investigate how
the disorder modifies the shape of the free energy curve: (1) We prove that, in
dimension d larger or equal to three 3, the presence of disorder makes the
phase transition at least of second order. This, in dimension larger or equal
to 4, contrasts with the fact that the phase transition of the annealed system
is of first order. (2) In any dimension, we prove that disorder modifies the
low temperature asymptotic of the free energy.Comment: 18 page
Motion and gravitational radiation of a binary system consisting of an oscillating and rotating coplanar dusty disk and a point-like object
A binary system composed of an oscillating and rotating coplanar dusty disk
and a point mass is considered. The conservative dynamics is treated on the
Newtonian level. The effects of gravitational radiation reaction and wave
emission are studied to leading quadrupole order. The related waveforms are
given. The dynamical evolution of the system is determined semi-analytically
exploiting the Hamiltonian equations of motion which comprise the effects both
of the Newtonian tidal interaction and the radiation reaction on the motion of
the binary system in elliptic orbits. Tidal resonance effects between orbital
and oscillatory motions are considered in the presence of radiation damping.Comment: 26 pages, 8 figure
Fractional moment bounds and disorder relevance for pinning models
We study the critical point of directed pinning/wetting models with quenched
disorder. The distribution K(.) of the location of the first contact of the
(free) polymer with the defect line is assumed to be of the form
K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a
(de)-localization phase transition: the free energy (per unit length) is zero
in the delocalized phase and positive in the localized phase. For \alpha<1/2 it
is known that disorder is irrelevant: quenched and annealed critical points
coincide for small disorder, as well as quenched and annealed critical
exponents. The same has been proven also for \alpha=1/2, but under the
assumption that L(.) diverges sufficiently fast at infinity, an hypothesis that
is not satisfied in the (1+1)-dimensional wetting model considered by Forgacs
et al. (1986) and Derrida et al. (1992), where L(.) is asymptotically constant.
Here we prove that, if 1/21, then quenched and annealed
critical points differ whenever disorder is present, and we give the scaling
form of their difference for small disorder. In agreement with the so-called
Harris criterion, disorder is therefore relevant in this case. In the marginal
case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at
infinity, we prove that the difference between quenched and annealed critical
points, which is known to be smaller than any power of the disorder strength,
is positive: disorder is marginally relevant. Again, the case considered by
Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and
remains open.Comment: 20 pages, 1 figure; v2: few typos corrected, references revised. To
appear on Commun. Math. Phy
Lovastatin Corrects Excess Protein Synthesis and Prevents Epileptogenesis in a Mouse Model of Fragile X Syndrome
Many neuropsychiatric symptoms of fragile X syndrome (FXS) are believed to be a consequence of altered regulation of protein synthesis at synapses. We discovered that lovastatin, a drug that is widely prescribed for the treatment of high cholesterol, can correct excess hippocampal protein synthesis in the mouse model of FXS and can prevent one of the robust functional consequences of increased protein synthesis in FXS, epileptogenesis. These data suggest that lovastatin is potentially disease modifying and could be a viable prophylactic treatment for epileptogenesis in FXS.FRAXA Research FoundationNational Institute of Mental Health (U.S.)Eunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.)Simons Foundatio
Hierarchical pinning models, quadratic maps and quenched disorder
We consider a hierarchical model of polymer pinning in presence of quenched
disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which
can be re-interpreted as an infinite dimensional dynamical system with random
initial condition (the disorder). It is defined through a recurrence relation
for the law of a random variable {R_n}_{n=1,2,...}, which in absence of
disorder (i.e., when the initial condition is degenerate) reduces to a
particular case of the well-known Logistic Map. The large-n limit of the
sequence of random variables 2^{-n} log R_n, a non-random quantity which is
naturally interpreted as a free energy, plays a central role in our analysis.
The model depends on a parameter alpha>0, related to the geometry of the
hierarchical lattice, and has a phase transition in the sense that the free
energy is positive if the expectation of R_0 is larger than a certain threshold
value, and it is zero otherwise. It was conjectured by Derrida et al. (1992)
that disorder is relevant (respectively, irrelevant or marginally relevant) if
1/2<alpha<1 (respectively, alpha<1/2 or alpha=1/2), in the sense that an
arbitrarily small amount of randomness in the initial condition modifies the
critical point with respect to that of the pure (i.e., non-disordered) model if
alpha is larger or equal to 1/2, but not if alpha is smaller than 1/2. Our main
result is a proof of these conjectures for the case alpha different from 1/2.
We emphasize that for alpha>1/2 we find the correct scaling form (for weak
disorder) of the critical point shift.Comment: 26 pages, 2 figures. v3: Theorem 1.6 improved. To appear on Probab.
Theory Rel. Field
On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature
We consider the Glauber dynamics for the 2D Ising model in a box of side L,
at inverse temperature and random boundary conditions whose
distribution P either stochastically dominates the extremal plus phase (hence
the quotation marks in the title) or is stochastically dominated by the
extremal minus phase. A particular case is when P is concentrated on the
homogeneous configuration identically equal to + (equal to -). For
large enough we show that for any there exists
such that the corresponding mixing time satisfies
. In the non-random case
(or ), this implies that . The same bound holds when the boundary conditions are all
+ on three sides and all - on the remaining one. The result, although still
very far from the expected Lifshitz behaviour , considerably
improves upon the previous known estimates of the form . The techniques are based on induction over length
scales, combined with a judicious use of the so-called "censoring inequality"
of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to
its equilibrium measure.Comment: 39 pages, 8 figures; v2: typos corrected, two references added. To
appear on Comm. Math. Phy
Estimating the parameters of the Sgr A* black hole
The measurement of relativistic effects around the galactic center may allow
in the near future to strongly constrain the parameters of the supermassive
black hole likely present at the galactic center (Sgr A*). As a by-product of
these measurements it would be possible to severely constrain, in addition,
also the parameters of the mass-density distributions of both the innermost
star cluster and the dark matter clump around the galactic center.Comment: Accepted for publication on General Relativity and Gravitation, 2010.
11 Pages, 1 Figur
One-loop chiral amplitudes of Moller scattering process
The high energy amplitudes of the large angles Moller scattering are
calculated in frame of chiral basis in Born and 1-loop QED level. Taking into
account as well the contribution from emission of soft real photons the compact
relations free from infrared divergences are obtained. The expressions for
separate chiral amplitudes contribution to the cross section are in agreement
with renormalization group predictions.Comment: 15 pages, 3 figure
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