1,471 research outputs found
Stability of Piecewise Deterministic Markovian Metapopulation Processes on Networks
The purpose of this paper is to study a Markovian metapopulation model on a
directed graph with edge-supported transfers and deterministic intra-nodal
population dynamics. We first state tractable stability conditions for two
typical frameworks motivated by applications: constant jump rates with
multiplicative transfer amplitudes, and coercive jump rates with unitary
transfers. More general criteria for boundedness, petiteness and ergodicity are
then given
Alien Calculus and non perturbative effects in Quantum Field Theory
In many domains of physics, methods are needed to deal with non-perturbative
aspects. I want here to argue that a good approach is to work on the Borel
transforms of the quantities of interest, the singularities of which give
non-perturbative contributions. These singularities in many cases can be
largely determined by using the alien calculus developed by Jean \'Ecalle. My
main example will be the two point function of a massless theory given as a
solution of a renormalization group equation.Comment: 4 pages, double-colum
Games orbits play and obstructions to Borel reducibility
We introduce a new, game-theoretic approach to anti-classification results
for orbit equivalence relations. Within this framework, we give a short
conceptual proof of Hjorth's turbulence theorem. We also introduce a new
dynamical criterion providing an obstruction to classification by orbits of CLI
groups. We apply this criterion to the relation of equality of countable sets
of reals, and the relations of unitary conjugacy of unitary and selfadjoint
operators on the separable infinite-dimensional Hilbert space.Comment: 13 pages. Final version, to appear in Groups, Geometry, and Dynamic
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