Wine Making for the Amateur

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Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

Holographic Dark Energy Characterized by the Total Comoving Horizon and Insights to Cosmological Constant and Coincidence Problem

The observed acceleration of the present universe is shown to be well explained by the holographic dark energy characterized by the total comoving horizon of the universe ($\eta$HDE). It is of interest to notice that the very large primordial part of the comoving horizon generated by the inflation of early universe makes the $\eta$HDE behave like a cosmological constant. As a consequence, both the fine-tuning problem and the coincidence problem can reasonably be understood with the inflationary universe and holographical principle. We present a systematic analysis and obtain a consistent cosmological constraint on the $\eta$HDE model based on the recent cosmological observations. It is found that the $\eta$HDE model gives the best-fit result $\Omega_{m0}=0.270$ ($\Omega_{de0}=0.730$) and the minimal $\chi^2_{min}=542.915$ which is compatible with $\chi^2_{\Lambda {\rm CDM}}=542.919$ for the $\Lambda$CDM model.Comment: 17 pages, 4 figures, two eqs. (26)(27) added for the consistent approximate solution of dark energy in early universe, references added, published version in PR

Generalized μ−τ\mu-\tau reflection symmetry and leptonic CP violation

We propose a generalized $\mu-\tau$ reflection symmetry to constrain the lepton flavor mixing parameters. We obtain a new correlation between the atmospheric mixing angle $\theta_{23}$ and the "Dirac" CP violation phase $\delta_{\rm CP}$. Only in a specific limit our proposed CP transformation reduces to standard $\mu-\tau$ reflection, for which $\theta_{23}$ and $\delta_{CP}$ are both maximal. The "Majorana" phases are predicted to lie at their CP-conserving values with important implications for the neutrinoless double beta decay rates. We also study the phenomenological implications of our scheme for present and future neutrino oscillation experiments including T2K, NO$\nu$A and DUNE.Comment: 14 pages, 9 figures, latex, Final version to appear in Physics Letters