Related papers: Randomstrasse101: Open Problems of 2025
$\texttt{Randomstrasse101}$ is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record of the Open Problems…
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
In this paper we study random optimization problems where random functions are investigated in sample paths. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.
In this note, convergence of random variables will be revisited. We will give the answers to 5 questions among the 6 open questions introduced in (Convergence rates in the law of large numbers and new kinds of convergence of random…
We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
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…
Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.
We discuss a connection between two areas of mathematics which until recently seemed to be rather distant from each other: (1) noncommutative harmonic analysis on groups and (2) some topics in probability theory related to random point…
Statistics 101, 201, and 202 are three open-source interactive web applications built with R \citep{R} and Shiny \citep{shiny} to support the teaching of introductory statistics and probability. The apps help students carry out common…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
These notes constitute the basis for the lectures given by the author at Centre de recherches math\'ematiques (CRM) at Universit\'e de Montreal, as part of the thematic semester on "Mathematical challenges in many-body physics and quantum…
The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For…