Irreducible vector-valued modular forms of dimension less than six

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension less than six. For representations of dimension less than four, it is shown that the associated space of vector-valued modular forms is a cyclic module over a certain skew polynomial ring of differential operators. For dimensions four and five, a complete list of possible Hilbert-Poincare series is given, using the fact that the space of vector-valued modular forms is a free module over the ring of classical modular forms for the full modular group. A mild restriction is then placed on the class of representation considered in these dimensions, and this again yields an explicit determination of the associated Hilbert-Poincare series.Comment: AMS-LaTeX, 32 pages. This version will appear in Illinois J. Mat

Structure of the module of vector-valued modular forms

Let $V$ be a representation of the modular group $\Gamma$ of dimension $p$. We show that the $\mathbb{Z}$-graded space $\mathcal{H}(V)$ of holomorphic vector-valued modular forms associated to $V$ is a free module of rank $p$ over the algebra $\mathcal{M}$ of classical holomorphic modular forms. We study the nature of $\mathcal{H}$ considered as a functor from $\Gamma$-modules to graded $\mathcal{M}$-lattices and give some applications, including the calculation of the Hilbert-Poincar\'{e} of $\mathcal{H}(V)$ in some cases

Quenched decay of correlations for slowly mixing systems

We study random towers that are suitable to analyse the statistics of slowly mixing random systems. We obtain upper bounds on the rate of quenched correlation decay in a general setting. We apply our results to the random family of Liverani-Saussol-Vaienti maps with parameters in $[\alpha_0,\alpha_1]\subset (0,1)$ chosen independently with respect to a distribution $\nu$ on $[\alpha_0,\alpha_1]$ and show that the quenched decay of correlation is governed by the fastest mixing map in the family. In particular, we prove that for every $\delta >0$, for almost every $\omega \in [\alpha_0,\alpha_1]^\mathbb Z$, the upper bound $n^{1-\frac{1}{\alpha_0}+\delta}$ holds on the rate of decay of correlation for H\"older observables on the fibre over $\omega$. For three different distributions $\nu$ on $[\alpha_0,\alpha_1]$ (discrete, uniform, quadratic), we also derive sharp asymptotics on the measure of return-time intervals for the quenched dynamics, ranging from $n^{-\frac{1}{\alpha_0}}$ to $(\log n)^{\frac{1}{\alpha_0}}\cdot n^{-\frac{1}{\alpha_0}}$ to $(\log n)^{\frac{2}{\alpha_0}}\cdot n^{-\frac{1}{\alpha_0}}$ respectively.Comment: Improved presentation and results (now only a>1 is needed and consequently $0<\alpha_0<1$ in the application for LSV maps

Covering Kids & Families Evaluation Case Study of Michigan: Exploring Medicaid and SCHIP Enrollment Trends and Their Links to Policy and Practice

Evaluates the impact in Michigan of the RWJF project to increase enrollment in Medicaid and State Children's Health Insurance Programs. Outlines state policy changes and local- and state-level findings on the links between activities and enrollment trend

Covering Kids & Families Evaluation: Case Study of Illinois: Exploring Links Between Policy, Practice and the Trends in New Medicaid/SCHIP Enrollments

Evaluates the impact in Illinois of the RWJF project to increase enrollment in Medicaid and State Children's Health Insurance Programs. Outlines state policy changes; outreach, simplification, and coordination activities; and 1999-2005 enrollment trends