Noticias en español
Non-bijective scaling limit of maps via restrictions.
Abstract: In recent years, scaling limits of random planar maps have been the subject of a lot of attention. So far, the convergence of these random combinatorial objects relies heavily on bijections. In this talk, I will present a non-bijective technique that allows to obtain the convergence of a random map model, using a convergent closely related random map model. Then, I will present a new result which is obtained using our technique: the Brownian disk is the limit of quadrangulations with a simple boundary, when the boundary is of order (faces^{1/2}).
Read MoreThe Ising model from the eyes of the Gaussian free field.
Abstract: The Ising model may be one of the most studied objects of statistical Physics. In recent years, it was shown that a proper renormalisation of a planar Ising model converges to a universal field: the continuous magnetisation field. This field is not a function but a Schwartz distribution, furthermore its statistics are not Gaussian. In this talk, we will study the properties of the Wick product of two independent magnetisation fields and show that they have the same law as a certain trigonometric function of the GFF. We will show how this correspondence allows us to find new...
Read MoreRandom walks on fractals and critical random
Resumen: The connections between random walks and electrical networks are well-known. I will describe work in this direction that demonstrates that if a sequence of spaces equipped with “resistance metrics” and measures converges with respect to the Gromov-Hausdorff -vague topology, and a certain non-explosion condition is satisfi ed, then the associated stochastic processes alsoconverge. This result generalises previous work on fractals and various models of randomgraphs in critical regimes. If time permits, I will also discuss associated time-changes and heat kernel estimates....
Read MoreGrowing Networks with Random Walks
Abstract: Network growth is a fundamental theme that has received much attention over the past decades. Various models that embody principles such as preferential attachment and local attachment rules have been proposed and studied. Among various approaches, random walks have been leveraged to capture such principles. In this work we propose and study the No Restart Random Walk (NRRW) model where a walker builds its network while moving around. In particular, after the walker takes s steps (a parameter) on the current network a new node with degree one is added to the network and...
Read MoreA martingale approach to convergence to the Kingman’s coalescente
Abstract: We consider the following dynamic. We start with a fix number of labeled, i.i.d. Markov chains over a finite state space, let the time pass, and when two chains meet, they behave as one chain. This dynamic induces a process in the set of partitions of the first natural numbers. We are interested in the asymptotic behavior of this process. On the late eighties J. T. Cox obtained some limit theorems for coalescing random walks on the discrete torus, when the Markov chains we considered before are simple random walks and we start with one random walk in each vertex of the torus....
Read MoreCost functionals for large random trees
Abstract : Additive tree functionals allow to represent the cost of many divide-and-conquer algorithms. We give an invariance principle for such tree functionals for the Catalan model and for simply generated trees . In the Catalan model, this relies on the natural embedding into the Brownian excursion. (Joint work with Jean-François Delmas and Marion Sciauveau)
Read More