On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process

In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower R\'enyi dimensions (entropy). Moreover, we show that the Tricot dimensions (packing dimension) equal the upper R\'enyi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when it is seen as a function of the distributed weights under the $\ell^{\infty}$ norm.Comment: 13 page

On the time schedule of Brownian Flights

We are interested on the statistics of the duration of Brownian diffusions started at distance \epsilon from a given boundary and stopped when they hit back the interface.Comment: 9 page

What is the Role of International Law in Global Health Governance on the Period of Covid-19

Rapid globalisation challenges many of the traditional assumptions about International law, which is linked to domestic law, especially the ways in which it is formed and the methods of its implementation. This phenomenon led governments to be more focused on international collaboration to achieve national public health purposes and succeed some audit over the cross-border powers that influence their populations. This essay will analyse the position on what is the role of international law in global health governance. Another significant result of this essay is that Global Actors should create a global health cooperation in order to implement the international law effectively on the period of Covid-19.

On Brownian flights

International audienceLet K be a compact subset of ${\mathbb R}^n$. We choose at random with uniform law a point at distance $\varepsilon$ of K and start a Brownian motion (BM) from this point. We study the probability that this BM hits K for the first time at a distance $\geq r$ from the starting point