相关论文: Random maps: proceeding of the Journ{\'e}es MAS 20…

A survey of reinforced random walk, with emphasis on the linear case.

Last two decades, the problem of robotic mapping has made a lot of progress in the research community. However, since the data provided by the sensor still contains noise, how to obtain an accurate map is still an open problem. In this…

Initial steps are presented towards understanding which finitely generated groups are almost surely generated as semigroups by the path of a random walk on the group.

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…

We use the order complex corresponding to a symmetric matrix (defined by Giusti et al in 2015). In this note, we use it to define a class of models of random graphs, and show some surprising experimental results, showing sharp phase…

This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)

The Krakow-Orsay collaboration has applied methods borrowed from equilibrium statistical mechanics and analytic combinatorics to study the geometry of random networks. Results contained in a series of recent publications and concerning…

In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.

The map-matching is an essential preprocessing step for most of the trajectory-based applications. Although it has been an active topic for more than two decades and, driven by the emerging applications, is still under development. There is…

This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.

This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years

Robotic Exploration has evolved rapidly in the past two decades as new and more complex techniques have been created to explore unknown regions efficiently. Exciting advancements in exploration, autonomous navigation, and sensor technology…

This is a survey of our work on embedded minimal disks.

Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic…

Random walks in cones have the double interest of being at the heart of many probabilistic problems and of being related to many mathematical fields, such as spectral theory, combinatorics, or discrete complex analysis. In this article, we…

Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.

This is a survey article to appear in the "Handbook on Teichmueller Theory".

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

The Martin boundary associated with the simple random walk on an example of partially oriented lattice is shown to be trivial by computing fine estimates of the Green kernel.

In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.