Abstract. We study the appearance of a novel phenomenon for linearly coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf b...

We prove that a uniform rooted plane map with n edges converges in distribution after a suitable normalization to the Brownian map for the Gromov–Hausdorff topology. A recent bijection due to Ambjørn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.

Consider the center of mass of a supercritical branching-Brownian motion, or that of a supercritical super-Brownian motion. In this paper we prove that it is a Brownian motion being slowed down such that it tends to a limiting position almost surely, which, in a sense complements a result of Tribe on the final behavior of a critical super-Brownian motion. This is shown to be true also for a mod...

Inspired by direct and indirect maximal center gauge methods which identify vortices in lattice calculations, using the connection formalism, we show that under some appropriate transformations, chains appear continuum limit of QCD vacuum.