Related papers: How to pick a random integer matrix? (and other qu…
Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large-N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.
We explore the following question: Is a decision-making program fair, for some useful definition of fairness? First, we describe how several algorithmic fairness questions can be phrased as program verification problems. Second, we discuss…
In this paper we study the probability that two elements selected at random with replacement from a given finite semigroup act the same by right translation on the semigroup, that is, the chosen elements have the same right matrix.
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
Can the behavior of a random matrix be improved by modifying a small fraction of its entries? Consider a random matrix $A$ with i.i.d. entries. We show that the operator norm of $A$ can be reduced to the optimal order $O(\sqrt{n})$ by…
We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…
This paper considers the challenge of designing football group draw mechanisms which have the uniform distribution over all valid draw assignments, but are also entertaining, practical, and transparent. We explain how to simulate the FIFA…
The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
The manuscript introduces a method to select a random sample from a stream by deciding on each sampling unit immediately after observing it. The process could be applied to unequal as well as equal probability sampling. The implementation…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
Processes to automate the selection of appropriate algorithms for various matrix computations are described. In particular, processes to check for, and certify, various matrix properties of black box matrices are presented. These include…
We discuss how to generate random unitary matrices from the classical compact groups U(N), O(N) and USp(N) with probability distributions given by the respective invariant measures. The algorithm is straightforward to implement using…
We address the problem of selecting $k$ representative nodes from a network, aiming to achieve two objectives: identifying the most influential nodes and ensuring the selection proportionally reflects the network's diversity. We propose two…