7,264 research outputs found
On the long time behavior of the TCP window size process
The TCP window size process appears in the modeling of the famous
Transmission Control Protocol used for data transmission over the Internet.
This continuous time Markov process takes its values in , is
ergodic and irreversible. It belongs to the Additive Increase Multiplicative
Decrease class of processes. The sample paths are piecewise linear
deterministic and the whole randomness of the dynamics comes from the jump
mechanism. Several aspects of this process have already been investigated in
the literature. In the present paper, we mainly get quantitative estimates for
the convergence to equilibrium, in terms of the Wasserstein coupling
distance, for the process and also for its embedded chain.Comment: Correction
Some simple but challenging Markov processes
In this note, we present few examples of Piecewise Deterministic Markov
Processes and their long time behavior. They share two important features: they
are related to concrete models (in biology, networks, chemistry,. . .) and they
are mathematically rich. Their math-ematical study relies on coupling method,
spectral decomposition, PDE technics, functional inequalities. We also relate
these simple examples to recent and open problems
Wigner Representation Theory of the Poincare Group, Localization, Statistics and the S-Matrix
It has been known that the Wigner representation theory for positive energy
orbits permits a useful localization concept in terms of certain lattices of
real subspaces of the complex Hilbert -space. This ''modular localization'' is
not only useful in order to construct interaction-free nets of local algebras
without using non-unique ''free field coordinates'', but also permits the study
of properties of localization and braid-group statistics in low-dimensional
QFT. It also sheds some light on the string-like localization properties of the
1939 Wigner's ''continuous spin'' representations.We formulate a constructive
nonperturbative program to introduce interactions into such an approach based
on the Tomita-Takesaki modular theory. The new aspect is the deep relation of
the latter with the scattering operator.Comment: 28 pages of LateX, removal of misprints and extension of the last
section. more misprints correcte
A L\'evy input fluid queue with input and workload regulation
We consider a queuing model with the workload evolving between consecutive
i.i.d.\ exponential timers according to a
spectrally positive L\'evy process that is reflected at zero, and
where the environment equals 0 or 1. When the exponential clock
ends, the workload, as well as the L\'evy input process, are modified; this
modification may depend on the current value of the workload, the maximum and
the minimum workload observed during the previous cycle, and the environment
of the L\'evy input process itself during the previous cycle. We analyse
the steady-state workload distribution for this model. The main theme of the
analysis is the systematic application of non-trivial functionals, derived
within the framework of fluctuation theory of L\'evy processes, to workload and
queuing models
K-theory and topological cyclic homology of henselian pairs
Given a henselian pair of commutative rings, we show that the
relative -theory and relative topological cyclic homology with finite
coefficients are identified via the cyclotomic trace . This
yields a generalization of the classical Gabber-Gillet-Thomason-Suslin rigidity
theorem (for mod coefficients, with invertible in ) and McCarthy's
theorem on relative -theory (when is nilpotent).
We deduce that the cyclotomic trace is an equivalence in large degrees
between -adic -theory and topological cyclic homology for a large class
of -adic rings. In addition, we show that -theory with finite
coefficients satisfies continuity for complete noetherian rings which are
-finite modulo . Our main new ingredient is a basic finiteness property
of with finite coefficients.Comment: 59 pages, revised and final versio
SGARFACE: A Novel Detector For Microsecond Gamma Ray Bursts
The Short GAmma Ray Front Air Cherenkov Experiment (SGARFACE) is operated at
the Whipple Observatory utilizing the Whipple 10m gamma-ray telescope. SGARFACE
is sensitive to gamma-ray bursts of more than 100MeV with durations from 100ns
to 35us and provides a fluence sensitivity as low as 0.8 gamma-rays per m^2
above 200MeV (0.05 gamma-rays per m^2 above 2GeV) and allows to record the
burst time structure.Comment: 29 pages, 14 figures, accepted for publication in Astroparticle
Physic
Motivations and Physical Aims of Algebraic QFT
We present illustrations which show the usefulness of algebraic QFT. In
particular in low-dimensional QFT, when Lagrangian quantization does not exist
or is useless (e.g. in chiral conformal theories), the algebraic method is
beginning to reveal its strength.Comment: 40 pages of LateX, additional remarks resulting from conversations
and mail contents, removal of typographical error
Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory
We investigate the continuum limit of the gauge-ball spectrum in the
four-dimensional pure U(1) lattice gauge theory. In the confinement phase we
identify various states scaling with the correlation length exponent . The square root of the string tension also scales with this
exponent, which agrees with the non-Gaussian fixed point exponent recently
found in the finite size studies of this theory. Possible scenarios for
constructing a non-Gaussian continuum theory with the observed gauge-ball
spectrum are discussed. The state, however, scales with a Gaussian
value . This suggests the existence of a second, Gaussian
continuum limit in the confinement phase and also the presence of a light or
possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb
phase we find evidence for a few gauge-balls, being resonances in multi-photon
channels; they seem to approach the continuum limit with as yet unknown
critical exponents. The maximal value of the renormalized coupling in this
phase is determined and its universality confirmed.Comment: 46 pages, 12 figure
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