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 G2G_2-MSSM - An MM Theory motivated model of Particle Physics

We continue our study of the low energy implications of $M$ theory vacua on $G_2$ 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 $G_2$-MSSM, can be naturally defined within the above framework. In this paper, we study some of the important phenomenological features of the $G_2$-MSSM. In particular, the soft supersymmetry breaking parameters and the superpartner spectrum are computed. The $G_2$-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 $G_2$-MSSM is also naturally consistent with precision gauge coupling unification. The phenomenological consequences for cosmology and collider physics of the $G_2$-MSSM will be reported in more detail soon.Comment: 42 pages, 7 figures, one figure corrected, reference adde