Infinite products of 2×22\times2 matrices and the Gibbs properties of Bernoulli convolutions

We consider the infinite sequences (A\_n)\_{n\in\NN} of $2\times2$ matrices with nonnegative entries, where the $A\_n$ are taken in a finite set of matrices. Given a vector V=\pmatrix{v\_1\cr v\_2} with $v\_1,v\_2>0$, we give a necessary and sufficient condition for $\displaystyle{A\_1... A\_nV\over|| A\_1... A\_nV||}$ to converge uniformly. In application we prove that the Bernoulli convolutions related to the numeration in Pisot quadratic bases are weak Gibbs

Grounds for Argument: Local Understandings, Science, and Global Processes in Special Forest Products Harvesting

In posing the question Where are the pickers? , Love and Jones suggest that the shifting paradigm in forestry is real and that academia is not leading the shift. Love and Jones illustrate the emergence of special forest products\u27 legitimacy in competing uses of forests with their experience and research in mushroom harvesting in the Pacific Northwest

Weak Gibbs property and system of numeration

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space \Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}. This space can be identified with the interval $[0,1]$ by means of the numeration in base $r$. The last section is devoted to the Bernoulli convolution in base $\beta={1+\sqrt5\over2}$, called the Erd\H os measure, and its analogue in base $-\beta=-{1+\sqrt5\over2}$, that we study by means of a suitable system of numeration

Coupling with the stationary distribution and improved sampling for colorings and independent sets

We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach. As an application, we show that for $k/\Delta >1.764$, the Glauber dynamics on $k$-colorings of a graph on $n$ vertices with maximum degree $\Delta$ converges in $O(n\log n)$ steps, assuming $\Delta =\Omega(\log n)$ and that the graph is triangle-free. Previously, girth $\ge 5$ was needed. As a second application, we give a polynomial-time algorithm for sampling weighted independent sets from the Gibbs distribution of the hard-core lattice gas model at fugacity $\lambda <(1-\epsilon)e/\Delta$, on a regular graph $G$ on $n$ vertices of degree $\Delta =\Omega(\log n)$ and girth $\ge 6$. The best known algorithm for general graphs currently assumes $\lambda <2/(\Delta -2)$.Comment: Published at http://dx.doi.org/10.1214/105051606000000330 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Party Platforms in Electoral Competition with many constituencies

This paper uses the Hotelling-Downs spatial model of electoral competition between candidates to explore competition between political parties. Two parties choose platforms in a unidimensional policy space, and then in a continuum of constituencies with different median voters candidates from the two parties compete in first-past-the-post elections. Departing from party platform is costly enough that candidates do not take the median voters preferred position in each constituency. In equilibrium, parties acting in their candidates best interests differentiate when one party locates right of center, the other prefers to locate strictly left of center to carve out a home turf,  consituencies that can be won with little to no deviation from party platform. Hence, Downsian competition that pulls candidates together pushes parties apart. Decreasing campaign costs  increases party differentiation as the leftist party must move further from the rightist party to carve out its home turf. For a range of costs, parties take more extreme positions than their most extreme candidates. For small costs, parties are too extreme to maximize voter welfare, whereas for large costs they are not extreme enough.electoral competition, spatial competition, Hotelling-Downs model