1,550 research outputs found
Concentration of empirical distribution functions with applications to non-i.i.d. models
The concentration of empirical measures is studied for dependent data, whose
joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev
inequalities. The general concentration results are then applied to spectral
empirical distribution functions associated with high-dimensional random
matrices.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ254 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
A Functional Form of the Isoperimetric Inequality for the Gaussian Measure
Let g be a smooth function on nwith values in [0, 1]. Using the isoperimetric property of the Gaussian measure, itis proved thatφ(Φ−1(Eg))−Eφ(Φ−1(g))⩽E; ∇g;. Conversely, this inequality implies the isoperimetric property of the Gaussian measure
Convergence to Stable Laws in Relative Entropy
Convergence to stable laws in relative entropy is established for sums of
i.i.d. random variables
A Functional Form of the Isoperimetric Inequality for the Gaussian Measure
Let g be a smooth function on nwith values in [0, 1]. Using the isoperimetric property of the Gaussian measure, itis proved thatφ(Φ−1(Eg))−Eφ(Φ−1(g))⩽E; ∇g;. Conversely, this inequality implies the isoperimetric property of the Gaussian measure
Optimal Concentration of Information Content For Log-Concave Densities
An elementary proof is provided of sharp bounds for the varentropy of random
vectors with log-concave densities, as well as for deviations of the
information content from its mean. These bounds significantly improve on the
bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543,
2011).Comment: 15 pages. Changes in v2: Remark 2.5 (due to C. Saroglou) added with
more general sufficient conditions for equality in Theorem 2.3. Also some
minor corrections and added reference
The -MSSM - An Theory motivated model of Particle Physics
We continue our study of the low energy implications of theory vacua on
manifolds, undertaken in \cite{Acharya:2007rc,Acharya:2006ia}, where it
was shown that the moduli can be stabilized and a TeV scale generated, with the
Planck scale as the only dimensionful input. A well-motivated phenomenological
model - the -MSSM, can be naturally defined within the above framework. In
this paper, we study some of the important phenomenological features of the
-MSSM. In particular, the soft supersymmetry breaking parameters and the
superpartner spectrum are computed. The -MSSM generically gives rise to
light gauginos and heavy scalars with wino LSPs when one tunes the cosmological
constant. Electroweak symmetry breaking is present but fine-tuned. The
-MSSM is also naturally consistent with precision gauge coupling
unification. The phenomenological consequences for cosmology and collider
physics of the -MSSM will be reported in more detail soon.Comment: 42 pages, 7 figures, one figure corrected, reference adde
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