Optimal quantization for infinite nonhomogeneous distributions on the real line

Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, an infinitely generated nonhomogeneous Borel probability measure $P$ is considered on $\mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th quantization error for every natural number $n$ is given. In addition, using the induction formula we give some results and observations about the optimal sets of $n$-means for all $n\geq 2$.Comment: arXiv admin note: text overlap with arXiv:1512.0037

Magnetoconductivity in chiral Lifshitz hydrodynamics

In this paper, based on the principles of linear response theory, we compute the longitudinal DC conductivity associated with Lifshitz like fixed points in the presence of chiral anomalies in ($3+1$) dimensions. In our analysis, apart from having the usual anomalous contributions due to chiral anomaly, we observe an additional and pure \textit{parity odd} effect to the magnetoconductivity which has its origin in the broken Lorentz (boost) invariance at a Lifshitz fixed point. We also device a holographic set up in order to compute ($z=2$) Lifshitz contributions to the magnetoconductivity precisely at strong coupling and low charge density limit.Comment: Minor clarifications added, Version To Appear In JHE

Holographic charge diffusion in non relativistic branes

In this paper, based on the principles of gauge/gravity duality and considering the so called \textit{hydrodynamic} limit we compute various charge transport properties for a class of strongly coupled non relativistic CFTs corresponding to $z=2$ fixed point whose dual gravitational counter part could be realized as the consistent truncation of certain non relativistic $Dp$ branes in the non extremal limit. From our analysis we note that unlike the case for the AdS black branes, the charge diffusion constant in the non relativistic background scales differently with the temperature. This shows a possible violation of the universal bound on the charge conductivity to susceptibility ratio in the context of non relativistic holography.Comment: 13 pages, clarificatons added, Version to appear in Physics Letters

Analytic integrability for strings on η \eta and λ \lambda deformed backgrounds

In this paper, based on simple analytic techniques, we explore the integrability conditions for classical stringy configurations defined over $\eta$ as well as $\lambda$- deformed backgrounds. We perform our analysis considering classical string motions within various subsectors of the full target space geometry. It turns out that classical string configurations defined over $\eta$- deformed backgrounds are non-integrable whereas on the other hand, the corresponding configurations are integrable over the $\lambda$- deformed background. Our analysis therefore imposes a strong constraint on the operator spectrum associated with the corresponding dual gauge theories at strong coupling.Comment: Version to appear in JHE