9,083 research outputs found
Markov loops, coverings and fields
We investigate the relations between the Poissonnian loop ensembles , their
occupation fields, non ramified Galois coverings of a graph, the associated
gauge fields, and random Eulerian networks
Sticky Particles and Stochastic Flows
Gaw\c{e}dzki and Horvai have studied a model for the motion of particles
carried in a turbulent fluid and shown that in a limiting regime with low
levels of viscosity and molecular diffusivity, pairs of particles exhibit the
phenomena of stickiness when they meet. In this paper we characterise the
motion of an arbitrary number of particles in a simplified version of their
model
Non-commutative covers and the modular group
We use non-commutative geometry to study the bulk of finite dimensional
representations of the modular group SL(2,Z). We give specific 2n-parameter
families of 6n-dimensional representations obtained from the quotient
singularity C^2/Z_6
Trees of semi-simple algebras
To a tree of semi-simple algebras we associate a qurve (or formally smooth
algebra) S. We introduce a Zariski- and etale quiver describing the finite
dimensional representations of S. In particular, we show that all quotient
varieties of the etale quiver have a natural Poisson structure induced by a
double Poisson algebra structure on a certain universal localization of its
path algebra. Explicit calculations are included for the group algebras of the
arithmetic groups (P)SL2(Z) and GL2(Z) but the methods apply as well to
congruence subgroups
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