KMS weights on higher rank buildings

We extend some of the results of Carey-Marcolli-Rennie on modular index invariants of Mumford curves to the case of higher rank buildings: we discuss notions of KMS weights on buildings, that generalize the construction of graph weights over graph C*-algebras.Comment: 25 pages, LaTeX, 4 jpg figure

An Improved Lower Bound for Sparse Reconstruction from Subsampled Hadamard Matrices

We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. We show that a matrix formed by uniformly subsampling rows of an $N \times N$ Hadamard matrix contains a $K$-sparse vector in the kernel, unless the number of subsampled rows is $\Omega(K \log K \log (N/K))$ --- our lower bound applies whenever $\min(K, N/K) > \log^C N$. Containing a sparse vector in the kernel precludes not only the restricted isometry property, but more generally the application of those matrices for uniform sparse recovery.Comment: Improved exposition and added an autho

Distribution of orders in number fields

In this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out our study, we use p-adic and motivic integration techniques to analyze the zeta function. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field. We also obtain non-trivial bounds for higher degree number fields

An Improved Lower Bound for Sparse Reconstruction from Subsampled Walsh Matrices

We give a short argument that yields a new lower bound on the number of uniformly and independently subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. We show that a matrix formed by uniformly and independently subsampling rows of an N ×N Walsh matrix contains a K-sparse vector in the kernel, unless the number of subsampled rows is Ω(KlogKlog(N/K)) — our lower bound applies whenever min(K,N/K) \u3e logC N. Containing a sparse vector in the kernel precludes not only the restricted isometry property, but more generally the application of those matrices for uniform sparse recovery