Related papers: New gaps on the Lagrange and Markov spectra

We prove a version of McDiarmid's bounded differences inequality for Markov chains, with constants proportional to the mixing time of the chain. We also show variance bounds and Bernstein-type inequalities for empirical averages of Markov…

Let M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Lambda(M) be the supremum of the bottom eigenvalue of the Laplacian of N, where N varies over all hyperbolic 3-manifolds homeomorphic to the…

Motivated by the recent observation of the high energy electron and positron excesses in cosmic ray by PAMELA and ATIC/PPB-BETS, we suggest an anomaly-free scenario for the universal extra dimension that localizes the SM quarks and splits…

In this note we will describe a simple and practical approach to get rigorous bounds on the Hausdorff dimension of limits sets for some one dimensional Markov iterated function schemes. The general problem has attracted considerable…

The aim of the project is to search for lithium in absorption at 6707.8 Angstroms to constrain the nature and the mass of the brightest low-metallicity L-type dwarfs (refered to as L subdwarfs) identified in large-scale surveys. We obtained…

We investigate the potential of leptonic meson decays $M \to \ell \bar\nu_\ell$, where $M$ is a pseudo-scalar meson, as a probe of neutrino portal dark matter. The model of our focus features a neutral fermion $\psi$ and scalar $\phi$,…

We present the first parallax and luminosity measurements for an L subdwarf, the sdL7 2MASS J05325346+8246465. Observations conducted over three years by the USNO infrared astrometry program yield an astrometric distance of 26.7+/-1.2 pc…

We investigate spectral properties of the Neumann Laplacian $\mathscr{A}_\varepsilon$ on a periodic unbounded domain $\Omega_\varepsilon$ depending on a small parameter $\varepsilon>0$. The domain $\Omega_\varepsilon$ is obtained by…

Motivated by the 750 GeV diphoton excess found at LHC, we compute the maximal width into $\gamma\gamma$ that a neutral scalar can acquire through a loop of charged fermions or scalars as function of the maximal scale at which the theory…

Let $(M,g)$ be a compact manifold and let $-\Delta \phi_k = \lambda_k \phi_k$ be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases:…

The Hoffman program with respect to any real or complex square matrix $M$ associated to a graph $G$ stems from A. J. Hoffman's pioneering work on the limit points for the spectral radius of adjacency matrices of graphs less than…

The existence of a strong spectral gap for lattices in semi-simple Lie groups is crucial in many applications. In particular, for arithmetic lattices it is useful to have bounds for the strong spectral gap that are uniform in the family of…

The determinant lower bound of Lovasz, Spencer, and Vesztergombi [European Journal of Combinatorics, 1986] is a powerful general way to prove lower bounds on the hereditary discrepancy of a set system. In their paper, Lovasz, Spencer, and…

Uncertainties of the MSSM predictions are due to an unknown SUSY breaking mechanism. To reduce these uncertainties, one usually imposes constraints on the MSSM parameter space. Recently, two new constraints became available, both from…

Using an ultra-deep blind survey with the MUSE integral field spectrograph on the ESO Very Large Telescope, we obtain spectroscopic redshifts to a depth never explored before: galaxies with observed magnitudes m > 30 - 32. Specifically, we…

It is well-known that numerically approximating calculus of variations problems possessing a Lavrentiev Gap Phenomenon (LGP) is challenging, and the standard numerical methodologies, such as finite element, finite difference, and…

Given $0\leq\alpha<1$, we define \[\begin{array}{lr} \mathbf{M}_\alpha f(u,v,t) = \sup_{ \mathbf{R} \ni (0,0,0)} {\rm vol} \{\mathbf{R}\}^{\alpha-1} \iiint_\mathbf{R}\left|f [(u,v,t)\odot(\xi,\eta,\tau)^{-1}]\right|d\xi d\eta d\tau…

The existence of a strong spectral gap for quotients $\Gamma\bs G$ of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming…

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, and let $U$ be a subset of $X$ whose complement is compact. We use the exponential mixing results for diagonalizable flows on $X$ to give upper estimates for the…

We update a previously-proposed set of supersymmetric benchmark scenarios, taking into account the precise constraints on the cold dark matter density obtained by combining WMAP and other cosmological data, as well as the LEP and b -> s…