Convergence to equilibrium for finite Markov processes, with application to the Random Energy Model

We estimate the distance in total variation between the law of a finite state Markov process at time t, starting from a given initial measure, and its unique invariant measure. We derive upper bounds for the time to reach the equilibrium. As an example of application we consider a special case of finite state Markov process in random environment: the Metropolis dynamics of the Random Energy Model. We also study the process of the environment as seen from the process

Carne--Varopoulos bounds for centered random walks

We extend the Carne--Varopoulos upper bound on the probability transitions of a Markov chain to a certain class of nonreversible processes by introducing the definition of a ``centering measure.'' In the case of random walks on a group, we study the connections between different notions of centering.Comment: Published at http://dx.doi.org/10.1214/009117906000000052 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

From Jack to Double Jack Polynomials via the Supersymmetric Bridge

The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine ${\widehat{\mathfrak {sl}}_2}$ algebra

Schur Superpolynomials: Combinatorial Definition and Pieri Rule

Schur superpolynomials have been introduced recently as limiting cases of the Macdonald superpolynomials. It turns out that there are two natural super-extensions of the Schur polynomials: in the limit $q=t=0$ and $q=t\rightarrow\infty$, corresponding respectively to the Schur superpolynomials and their dual. However, a direct definition is missing. Here, we present a conjectural combinatorial definition for both of them, each being formulated in terms of a distinct extension of semi-standard tableaux. These two formulations are linked by another conjectural result, the Pieri rule for the Schur superpolynomials. Indeed, and this is an interesting novelty of the super case, the successive insertions of rows governed by this Pieri rule do not generate the tableaux underlying the Schur superpolynomials combinatorial construction, but rather those pertaining to their dual versions. As an aside, we present various extensions of the Schur bilinear identity

Co-reduction of aluminium and lanthanide ions in molten fluorides : application to cerium and samarium extraction from nuclear waste

This work concerns the method of co-reduction process with aluminium ions in LiF–CaF2 medium (79–21 mol.%) on tungsten electrode for cerium and samarium extraction. Electrochemical techniques such as cyclic and square wave voltammetries, and potentiostatic electrolyses were used to study the co-reduction of CeF3 and SmF3 with AlF3. For each of these elements, specific peaks of Al–Ce and Al–Sm alloys formationwere observed by voltammetry aswell as peaks of pure cerium and aluminium, and pure samarium and aluminium respectively. The difference of potential measured between the solvent reduction and the alloy formation suggests expecting an extraction efficiency of 99.99% of each lanthanide by the process. Different intermetallic compounds were obtained for different potentiostatic electrolysis and were characterised by Scanning Electron Microscopy with EDS probe. The validity of the process was verified by carrying out cerium and samarium extractions in the form of Al–Ln alloy; the extraction efficiency was 99.5% for Ce(III) and 99.4% for Sm(III)