Category
Polynomials
Related publications (387)
A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM
Thomas Mountford, Michael Cranston
In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...
Providence2023Lattice packings through division algebras
In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...
SPRINGER HEIDELBERG2023Revisiting Offline Compression: Going Beyond Factorization-based Methods for Transformer Language Models
Karl Aberer, Rémi Philippe Lebret, Mohammadreza Banaei
Recent transformer language models achieve outstanding results in many natural language processing (NLP) tasks. However, their enormous size often makes them impractical on memory-constrained devices, requiring practitioners to compress them to smaller net ...
Assoc Computational Linguistics-Acl2023Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups
We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...
SPRINGER HEIDELBERG2023Multiplicity-free representations of algebraic groups II
Donna Testerman, Martin W. Liebeck
We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2022Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups
Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...
EPFL2022Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
AMER MATHEMATICAL SOC2022A Determinantal Identity for the Permanent of a Rank 2 Matrix
We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...
TAYLOR & FRANCIS INC2022Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation
In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices.In the first part, we consider algorithms for building l ...
EPFL2022From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem
In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...
EPFL2022