Confidence intervals for the critical value in the divide and color model

We obtain confidence intervals for the location of the percolation phase transition in H\"aggstr\"om's divide and color model on the square lattice $\mathbb{Z}^2$ and the hexagonal lattice $\mathbb{H}$. The resulting probabilistic bounds are much tighter than the best deterministic bounds up to date; they give a clear picture of the behavior of the DaC models on $\mathbb{Z}^2$ and $\mathbb{H}$ and enable a comparison with the triangular lattice $\mathbb{T}$. In particular, our numerical results suggest similarities between DaC model on these three lattices that are in line with universality considerations, but with a remarkable difference: while the critical value function $r_c(p)$ is known to be constant in the parameter $p$ for $p<p_c$ on $\mathbb{T}$ and appears to be linear on $\mathbb{Z}^2$, it is almost certainly non-linear on $\mathbb{H}$

Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order

We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.Comment: 37 pages, 14 figure

Analysis of non ambiguous BOC signal acquisition performance Acquisition

The Binary Offset Carrier planned for future GNSS signal, including several GALILEO Signals as well as GPS M-code, presents a high degree of spectral separation from conventional signals. It also greatly improves positioning accuracy and enhances multipath rejection. However, with such a modulation, the acquisition process is made more complex. Specific techniques must be employed in order to avoid unacceptable errors. This paper assesses the performance of three method allowing to acquire and track BOC signal unambiguously : The Bump-jumping technique, The "BPSK-like" technique and the subcarrier Phase cancellation technique

A Proof of the S-m-n theorem in Coq

This report describes the implementation of a mechanisation of the theory of computation in the Coq proof assistant which leads to a proof of the Smn theorem. This mechanisation is based on a model of computation similar to the partial recursive function model and includes the definition of a computable function, proofs of the computability of a number of functions and the definition of an effective coding from the set of partial recursive functions to natural numbers. This work forms part of a comparative study of the HOL and Coq proof assistants

Proliferating parasites in dividing cells : Kimmel's branching model revisited

We consider a branching model introduced by Kimmel for cell division with parasite infection. Cells contain proliferating parasites which are shared randomly between the two daughter cells when they divide. We determine the probability that the organism recovers, meaning that the asymptotic proportion of contaminated cells vanishes. We study the tree of contaminated cells, give the asymptotic number of contaminated cells and the asymptotic proportions of contaminated cells with a given number of parasites. This depends on domains inherited from the behavior of branching processes in random environment (BPRE) and given by the bivariate value of the means of parasite offsprings. In one of these domains, the convergence of proportions holds in probability, the limit is deterministic and given by the Yaglom quasistationary distribution. Moreover, we get an interpretation of the limit of the Q-process as the size-biased quasistationary distribution

Hausdorff dimensions for SLE_6

We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all \kappa<8, the SLE_{\kappa} trace has cut-points.Comment: Published at http://dx.doi.org/10.1214/009117904000000072 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org