10,557 research outputs found
Mod-discrete expansions
In this paper, we consider approximating expansions for the distribution of
integer valued random variables, in circumstances in which convergence in law
cannot be expected. The setting is one in which the simplest approximation to
the 'th random variable is by a particular member of a given
family of distributions, whose variance increases with . The basic
assumption is that the ratio of the characteristic function of and that
of R_n$ converges to a limit in a prescribed fashion. Our results cover a
number of classical examples in probability theory, combinatorics and number
theory
Bagchi's Theorem for families of automorphic forms
We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem
for family of primitive cusp forms of weight and prime level, and discuss
under which conditions the argument will apply to general reasonable family of
automorphic -functions.Comment: 15 page
Mod-Gaussian convergence and the value distribution of and related quantities
In the context of mod-Gaussian convergence, as defined previously in our work
with J. Jacod, we obtain lower bounds for local probabilities for a sequence of
random vectors which are approximately Gaussian with increasing covariance.
This is motivated by the conjecture concerning the density of the set of values
of the Riemann zeta function on the critical line. We obtain evidence for this
fact, and derive unconditional results for random matrices in compact classical
groups, as well as for certain families of L-functions over finite fields.Comment: 26 pages, 2 figures, v3: stronger quantitative statements and other
change
Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"
It is shown by examples that the position uncertainty on a circle, proposed
recently by Kowalski and Rembieli\'nski [J. Phys. A 35 (2002) 1405] is not
consistent with the state localization. We argue that the relevant
uncertainties and uncertainty relations (UR's) on a circle are that based on
the Gram-Robertson matrix. Several of these generalized UR's are displayed and
related criterions for squeezed states are discussed.Comment: 5 pages, LaTex2e, 3 figures.ep
Wick ordering for coherent state quantization in 1+1 de Sitter space
We show that the coherent state quantization of massive particles in 1+1 de
Sitter space exhibits an ordering property: There exist some classical
observables and such that , where is the quantum observable corresponding to the classical
observable .Comment: Accepted in Phys. Lett.
Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of
signature (2s,s) which are not locally homogeneous but whose curvature tensors
never the less exhibit a number of important symmetry properties. They are
curvature homogeneous; their curvature tensor is modeled on that of a local
symmetric space. They are spacelike Jordan Osserman with a Jacobi operator
which is nilpotent of order 3; they are not timelike Jordan Osserman. They are
k-spacelike higher order Jordan Osserman for ; they are k-timelike
higher order Jordan Osserman for , and they are not k timelike
higher order Jordan Osserman for .Comment: Update bibliography, fix minor misprint
2+1 gravity and Doubly Special Relativity
It is shown that gravity in 2+1 dimensions coupled to point particles
provides a nontrivial example of Doubly Special Relativity (DSR). This result
is obtained by interpretation of previous results in the field and by
exhibiting an explicit transformation between the phase space algebra for one
particle in 2+1 gravity found by Matschull and Welling and the corresponding
DSR algebra. The identification of 2+1 gravity as a system answers a
number of questions concerning the latter, and resolves the ambiguity of the
basis of the algebra of observables.
Based on this observation a heuristic argument is made that the algebra of
symmetries of ultra high energy particle kinematics in 3+1 dimensions is
described by some DSR theory.Comment: 8 pages Latex, no figures, typos correcte
Quantitative sheaf theory
We introduce a notion of complexity of a complex of ell-adic sheaves on a
quasi-projective variety and prove that the six operations are "continuous", in
the sense that the complexity of the output sheaves is bounded solely in terms
of the complexity of the input sheaves. A key feature of complexity is that it
provides bounds for the sum of Betti numbers that, in many interesting cases,
can be made uniform in the characteristic of the base field. As an
illustration, we discuss a few simple applications to horizontal
equidistribution results for exponential sums over finite fields.Comment: v3, 68 pages; the key ideas of this paper are due to W. Sawin; A.
Forey, J. Fres\'an and E. Kowalski drafted the current version of the text;
revised after referee report
No Drama Quantum Electrodynamics?
This article builds on recent work (A. Akhmeteli, Int'l Journ. of Quantum
Information, vol. 9, Suppl. (2011) p. 17, and A. Akhmeteli, Journ. Math. Phys.,
vol. 52 (2011) p. 082303), providing a theory that is based on spinor
electrodynamics, is described by a system of partial differential equations in
3+1 dimensions, but reproduces unitary evolution of a quantum field theory in
the Fock space. To this end, after introduction of a complex four-potential of
electromagnetic field, which generates the same electromagnetic fields as the
initial real four-potential, spinor field is algebraically eliminated from the
equations of spinor electrodynamics. It is proven that the resulting equations
for electromagnetic field describe independent evolution of the latter and can
be embedded into a quantum field theory using a generalized Carleman
linearization procedure. The theory provides a simple and at least reasonably
realistic model, valuable for interpretation of quantum theory. The issues
related to the Bell theorem are discussed.Comment: 9 pages, no figures. Published in European Physical Journal C. A
clarification is added at the end of Section III. The journal version is at
http://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-013-2371-4.pdf
(open access
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