1,047 research outputs found
Family of solvable generalized random-matrix ensembles with unitary symmetry
We construct a very general family of characteristic functions describing
Random Matrix Ensembles (RME) having a global unitary invariance, and
containing an arbitrary, one-variable probability measure which we characterize
by a `spread function'. Various choices of the spread function lead to a
variety of possible generalized RMEs, which show deviations from the well-known
Gaussian RME originally proposed by Wigner. We obtain the correlation functions
of such generalized ensembles exactly, and show examples of how particular
choices of the spread function can describe ensembles with arbitrary eigenvalue
densities as well as critical ensembles with multifractality.Comment: 4 pages, to be published in Phys. Rev. E, Rapid Com
Mod-Gaussian convergence and its applications for models of statistical mechanics
In this paper we complete our understanding of the role played by the
limiting (or residue) function in the context of mod-Gaussian convergence. The
question about the probabilistic interpretation of such functions was initially
raised by Marc Yor. After recalling our recent result which interprets the
limiting function as a measure of "breaking of symmetry" in the Gaussian
approximation in the framework of general central limit theorems type results,
we introduce the framework of -mod-Gaussian convergence in which the
residue function is obtained as (up to a normalizing factor) the probability
density of some sequences of random variables converging in law after a change
of probability measure. In particular we recover some celebrated results due to
Ellis and Newman on the convergence in law of dependent random variables
arising in statistical mechanics. We complete our results by giving an
alternative approach to the Stein method to obtain the rate of convergence in
the Ellis-Newman convergence theorem and by proving a new local limit theorem.
More generally we illustrate our results with simple models from statistical
mechanics.Comment: 49 pages, 21 figure
Modeling Global Warming Scenarios in Greenback Cutthroat Trout (\u3cem\u3eOncorhynchus Clarki Stomias\u3c/em\u3e) Streams: Implications for Species Recovery
Changes in global climate may exacerbate other anthropogenic stressors, accelerating the decline in distribution and abundance of rare species throughout the world. We examined the potential effects of a warming climate on the greenback cutthroat trout (Oncorhynchus clarki stomias), a resident salmonid that inhabits headwater streams of the central Rocky Mountains. Greenbacks are outcompeted at lower elevations by nonnative species of trout and currently are restricted to upper-elevation habitats where barriers to upstream migration by nonnatives are or have been established. We used likelihood-based techniques and information theoretics to select models predicting stream temperature changes for 10 streams where greenback cutthroat trout have been translocated. These models showed high variability among responses by different streams, indicating the usefulness of a stream-specific approach. We used these models to project changes in stream temperatures based on 2°C and 4°C warming of average air temperatures. In these warming scenarios, spawning is predicted to begin from 2 to 3.3 weeks earlier than would be expected under baseline conditions. Of the 10 streams used in this assessment, 5 currently have less than a 50% chance of translocation success. Warming increased the probability of translocation success in these 5 streams by 11.2% and 21.8% in the 2 scenarios, respectively. Assuming barriers to upstream migration by nonnative competitors maintain their integrity, we conclude that an overall habitat improvement results because greenbacks have been restricted through competition with nonnatives to suboptimal habitats, which are generally too cold to be highly productive
A general central limit theorem and a subsampling variance estimator for 뱉mixing point processes
Lipoxin A4 stable analogs reduce allergic airway responses via mechanisms distinct from CysLT1 receptor antagonism
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154665/1/fsb2fj078653com.pd
Integrated random processes exhibiting long tails, finite moments and 1/f spectra
A dynamical model based on a continuous addition of colored shot noises is
presented. The resulting process is colored and non-Gaussian. A general
expression for the characteristic function of the process is obtained, which,
after a scaling assumption, takes on a form that is the basis of the results
derived in the rest of the paper. One of these is an expansion for the
cumulants, which are all finite, subject to mild conditions on the functions
defining the process. This is in contrast with the Levy distribution -which can
be obtained from our model in certain limits- which has no finite moments. The
evaluation of the power spectrum and the form of the probability density
function in the tails of the distribution shows that the model exhibits a 1/f
spectrum and long tails in a natural way. A careful analysis of the
characteristic function shows that it may be separated into a part representing
a Levy processes together with another part representing the deviation of our
model from the Levy process. This allows our process to be viewed as a
generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.
Bringing the margins into the middle:Reflections on racism, class and the racialized outsider
This paper explores Virdeeâs account of how racialized minorities in socialist movements âplayed an instrumental role in trying to align struggles against racism with those against class exploitationâ (p. 164). In so doing, Virdee makes an important intervention at a time when popular historians and other ideologues are colluding in the elevation of myths and â no doubt in their view â noble lies that preclude these stories. Moving through theoretical debates concerning the relationships between race and class, the nature and form of sociologies of âoutsidersâ, to political issues of mobilization, Virdeeâs book successfully brings in from the margins an account the multi-ethnic character of the working class in England from the very moment of its inception
The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
The main purpose of the paper is an essentially probabilistic analysis of
relativistic quantum mechanics. It is based on the assumption that whenever
probability distributions arise, there exists a stochastic process that is
either responsible for temporal evolution of a given measure or preserves the
measure in the stationary case. Our departure point is the so-called
Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique
Markov stochastic interpolation between any given pair of boundary probability
densities for a process covering a fixed, finite duration of time, provided we
have decided a priori what kind of primordial dynamical semigroup transition
mechanism is involved. In the nonrelativistic theory, including quantum
mechanics, Feyman-Kac-like kernels are the building blocks for suitable
transition probability densities of the process. In the standard "free" case
(Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered.
In the framework of the Schr\"{o}dinger problem, the "free noise" can also be
extended to any infinitely divisible probability law, as covered by the
L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians
and are known to generate such laws, we focus on
them for the analysis of probabilistic phenomena, which are shown to be
associated with the relativistic wave (D'Alembert) and matter-wave
(Klein-Gordon) equations, respectively. We show that such stochastic processes
exist and are spatial jump processes. In general, in the presence of external
potentials, they do not share the Markov property, except for stationary
situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger
evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil
A Grassmann integral equation
The present study introduces and investigates a new type of equation which is
called Grassmann integral equation in analogy to integral equations studied in
real analysis. A Grassmann integral equation is an equation which involves
Grassmann integrations and which is to be obeyed by an unknown function over a
(finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann
integral equations is explicitly studied for certain low-dimensional Grassmann
algebras. The choice of the equation under investigation is motivated by the
effective action formalism of (lattice) quantum field theory. In a very general
setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional
analogues of the generating functionals of the Green functions are worked out
explicitly by solving a coupled system of nonlinear matrix equations. Finally,
by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi},
{\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the
generators of the Grassmann algebra G_2n), between the finite-dimensional
analogues G_0 and G of the (``classical'') action and effective action
functionals, respectively, a special Grassmann integral equation is being
established and solved which also is equivalent to a coupled system of
nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann
integral equation exist for n=2 (and consequently, also for any even value of
n, specifically, for n=4) but not for n=3. If \lambda=1, the considered
Grassmann integral equation has always a solution which corresponds to a
Gaussian integral, but remarkably in the case n=4 a further solution is found
which corresponds to a non-Gaussian integral. The investigation sheds light on
the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the
reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54],
[61], [64], [139] added
Quantum Zeno Effect and Light-Dark Periods for a Single Atom
The quantum Zeno effect (QZE) predicts a slow-down of the time development of
a system under rapidly repeated ideal measurements, and experimentally this was
tested for an ensemble of atoms using short laser pulses for non-selective
state measurements. Here we consider such pulses for selective measurements on
a single system. Each probe pulse will cause a burst of fluorescence or no
fluorescence. If the probe pulses were strictly ideal measurements, the QZE
would predict periods of fluorescence bursts alternating with periods of no
fluorescence (light and dark periods) which would become longer and longer with
increasing frequency of the measurements. The non-ideal character of the
measurements is taken into account by incorporating the laser pulses in the
interaction, and this is used to determine the corrections to the ideal case.
In the limit, when the time between the laser pulses goes to zero, no freezing
occurs but instead we show convergence to the familiar macroscopic light and
dark periods of the continuously driven Dehmelt system. An experiment of this
type should be feasible for a single atom or ion in a trapComment: 16 pages, LaTeX, a4.sty; to appear in J. Phys.
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