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Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Breiman's (2001) random forests are a very popular class of learning algorithms often able to produce good predictions even in high-dimensional frameworks, with no need to accurately tune its inner parameters. Unfortunately, there are no theoretical findings to support the default values used for these parameters in Breiman's algorithm. The aim of this paper is therefore to present recent theoretical results providing some insights on the role and the tuning of these parameters. [ABSTRACT FROM AUTHOR]

This paper is devoted to non-cooperative games in idempotent measures. We consider two kinds of such games. Firstly, players are allowed to play their mixed idempotent strategies. We also consider games where belief of each player about a choice of the strategy by the other players is an idempotent measure. We prove existence of equilibria in both cases and discuss the difference between them. [ABSTRACT FROM AUTHOR]

Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The first talk at the session Random trees and random forests "Journée MAS" (27/08/2021) was presented by I. Kortchemski. After a general up-to-date introduction to local and scaling limits of Bienaymé trees (which are discrete branching trees), he presented new results on precise behavior of the largest out-degree of large branching trees when the offspring distribution μ is subcritical with μ(n) of order n−β for large n and β > 2 or critical with μ(n) of order n−2. In the next talk, M. Nassif gave asymptotics of additive functionals of large Bienayme trees in the global regime, which can be understood using scaling limits. Looking at Cayley trees with fixed size, A. Contat established a surprising identity for randomly built independent sets. Eventually J.-J. Duchamps presented some results on the distribution of the discrete Moran forest, a random graph arising in a classical population model at equilibrium. [ABSTRACT FROM AUTHOR]

In this paper, we are interested by advanced backward stochastic differential equations (ABSDEs), in a probability space equipped with a Brownian motion and a single jump process, with a jump at time τ. ABSDEs are BSDEs where the driver depends on the future paths of the solution. We show, that under immersion hypothesis between the Brownian filtration and its progressive enlargement with τ, assuming that the conditional law of τ is equivalent to the unconditional law of τ, and a Lipschitz condition on the driver, the ABSDE has a solution. [ABSTRACT FROM AUTHOR]

We improve the results about the well-posedness of the regularized fractional dispersive equation (1 + Dxα)ut + ux + uux = 0 when 0 < α ≤ 1. When #x03B1; < 1, the existence and uniqueness of vanishing viscosity solution is proved. [ABSTRACT FROM AUTHOR]

We present what the title says with an emphasis on separation and topological properties as they relate to some of the fundamental principles of nonlinear analysis. [ABSTRACT FROM AUTHOR]