558 research outputs found
Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime
In this paper we derive a technique of obtaining limit theorems for suprema
of L\'evy processes from their random walk counterparts. For each , let
be a sequence of independent and identically distributed
random variables and be a L\'evy processes such that
, and as . Let .
Then, under some mild assumptions, , for some random variable and some function
. We utilize this result to present a number of limit theorems
for suprema of L\'evy processes in the heavy-traffic regime
On the Thermodynamic Limit in Random Resistors Networks
We study a random resistors network model on a euclidean geometry \bt{Z}^d.
We formulate the model in terms of a variational principle and show that, under
appropriate boundary conditions, the thermodynamic limit of the dissipation per
unit volume is finite almost surely and in the mean. Moreover, we show that for
a particular thermodynamic limit the result is also independent of the boundary
conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty',
revised version to appear in Journal of Physics
Strange-Beauty Meson Production at Colliders
The production rates and transverse momentum distributions of the
strange-beauty mesons and at colliders are calculated
assuming fragmentation is the dominant process. Results are given for the
Tevatron in the large transverse momentum region, where fragmentation is
expected to be most important.Comment: Minor changes in the discussion section. Also available at
http://www.ph.utexas.edu/~cheung/paper.htm
Comments on SUSY inflation models on the brane
In this paper we consider a class of inflation models on the brane where the
dominant part of the inflaton scalar potential does not depend on the inflaton
field value during inflation. In particular, we consider supernatural
inflation, its hilltop version, A-term inflation, and supersymmetric (SUSY) D-
and F-term hybrid inflation on the brane. We show that the parameter space can
be broadened, the inflation scale generally can be lowered, and still possible
to have the spectral index .Comment: 7 page
Dual random fragmentation and coagulation and an application to the genealogy of Yule processes
The purpose of this work is to describe a duality between a fragmentation
associated to certain Dirichlet distributions and a natural random coagulation.
The dual fragmentation and coalescent chains arising in this setting appear in
the description of the genealogy of Yule processes.Comment: 14 page
On exact time-averages of a massive Poisson particle
In this work we study, under the Stratonovich definition, the problem of the
damped oscillatory massive particle subject to a heterogeneous Poisson noise
characterised by a rate of events, \lambda (t), and a magnitude, \Phi,
following an exponential distribution. We tackle the problem by performing
exact time-averages over the noise in a similar way to previous works analysing
the problem of the Brownian particle. From this procedure we obtain the
long-term equilibrium distributions of position and velocity as well as
analytical asymptotic expressions for the injection and dissipation of energy
terms. Considerations on the emergence of stochastic resonance in this type of
system are also set forth.Comment: 21 pages, 5 figures. To be published in Journal of Statistical
Mechanics: Theory and Experimen
Observable Optimal State Points of Sub-additive Potentials
For a sequence of sub-additive potentials, Dai [Optimal state points of the
sub-additive ergodic theorem, Nonlinearity, 24 (2011), 1565-1573] gave a method
of choosing state points with negative growth rates for an ergodic dynamical
system. This paper generalizes Dai's result to the non-ergodic case, and proves
that under some mild additional hypothesis, one can choose points with negative
growth rates from a positive Lebesgue measure set, even if the system does not
preserve any measure that is absolutely continuous with respect to Lebesgue
measure.Comment: 16 pages. This work was reported in the summer school in Nanjing
University. In this second version we have included some changes suggested by
the referee. The final version will appear in Discrete and Continuous
Dynamical Systems- Series A - A.I.M. Sciences and will be available at
http://aimsciences.org/journals/homeAllIssue.jsp?journalID=
Higgs Boson Sector of the Next-to-MSSM with CP Violation
We perform a comprehensive study of the Higgs sector in the framework of the
next-to-minimal supersymmetric standard model with CP-violating parameters in
the superpotential and in the soft-supersymmetry-breaking sector. Since the CP
is no longer a good symmetry, the two CP-odd and the three CP-even Higgs bosons
of the next-to-minimal supersymmetric standard model in the CP-conserving limit
will mix. We show explicitly how the mass spectrum and couplings to gauge
bosons of the various Higgs bosons change when the CP-violating phases take on
nonzero values. We include full one-loop and the logarithmically enhanced
two-loop effects employing the renormalization-group (RG) improved approach. In
addition, the LEP limits, the global minimum condition, and the positivity of
the square of the Higgs-boson mass have been imposed. We demonstrate the
effects on the Higgs-mass spectrum and the couplings to gauge bosons with and
without the RG-improved corrections. Substantial modifications to the allowed
parameter space happen because of the changes to the Higgs-boson spectrum and
their couplings with the RG-improved corrections. Finally, we calculate the
mass spectrum and couplings of the few selected scenarios and compare to the
previous results in literature where possible; in particular, we illustrate a
scenario motivated by electroweak baryogenesis.Comment: 40 pages, 49 figures; v2: typos corrected and references added; v3:
some clarification and new figures added, version published in PR
Infectious Default Model with Recovery and Continuous Limit
We introduce an infectious default and recovery model for N obligors.
Obligors are assumed to be exchangeable and their states are described by N
Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying
independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery
infections are described by Y_{ij} and Y'_{ij}. We obtain the default
probability function P(k) for k defaults. Taking its continuous limit, we find
two nontrivial probability distributions with the reflection symmetry of S_{i}
\leftrightarrow 1-S_{i}. Their profiles are singular and oscillating and we
understand it theoretically. We also compare P(k) with an implied default
distribution function inferred from the quotes of iTraxx-CJ. In order to
explain the behavior of the implied distribution, the recovery effect may be
necessary.Comment: 13 pages, 7 figure
Expected length of the longest common subsequence for large alphabets
We consider the length L of the longest common subsequence of two randomly
uniformly and independently chosen n character words over a k-ary alphabet.
Subadditivity arguments yield that the expected value of L, when normalized by
n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville
from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe
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