[图书][B] Random graphs and complex networks
R Van Der Hofstad - 2024 - books.google.com
Complex networks are key to describing the connected nature of the society that we live in.
This book, the second of two volumes, describes the local structure of random graph models …
This book, the second of two volumes, describes the local structure of random graph models …
[图书][B] Random matrix methods for machine learning
R Couillet, Z Liao - 2022 - books.google.com
This book presents a unified theory of random matrices for applications in machine learning,
offering a large-dimensional data vision that exploits concentration and universality …
offering a large-dimensional data vision that exploits concentration and universality …
Recent progress in combinatorial random matrix theory
VH Vu - 2021 - projecteuclid.org
Recent progress in combinatorial random matrix theory Page 1 Probability Surveys Vol. 18 (2021)
179–200 ISSN: 1549-5787 https://doi.org/10.1214/20-PS346 Recent progress in combinatorial …
179–200 ISSN: 1549-5787 https://doi.org/10.1214/20-PS346 Recent progress in combinatorial …
On the phase transition in random simplicial complexes
It is well known that the G (n, p) model of random graphs undergoes a dramatic change
around p=1n. It is here that the random graph, almost surely, contains cycles, and here it first …
around p=1n. It is here that the random graph, almost surely, contains cycles, and here it first …
Matchings on infinite graphs
Abstract Elek and Lippner (Proc. Am. Math. Soc. 138 (8), 2939–2947, 2010) showed that the
convergence of a sequence of bounded-degree graphs implies the existence of a limit for …
convergence of a sequence of bounded-degree graphs implies the existence of a limit for …
On the concrete security of Goldreich's pseudorandom generator
Local pseudorandom generators allow to expand a short random string into a long pseudo-
random string, such that each output bit depends on a constant number d of input bits. Due …
random string, such that each output bit depends on a constant number d of input bits. Due …
Sparse expanders have negative curvature
J Salez - Geometric and Functional Analysis, 2022 - Springer
We prove that bounded-degree expanders with non-negative Ollivier–Ricci curvature do not
exist, thereby solving a long-standing open problem suggested by A. Naor and E. Milman …
exist, thereby solving a long-standing open problem suggested by A. Naor and E. Milman …
The exact rank of sparse random graphs
Two landmark results in combinatorial random matrix theory, due to Koml\'os and Costello-
Tao-Vu, show that discrete random matrices and symmetric discrete random matrices are …
Tao-Vu, show that discrete random matrices and symmetric discrete random matrices are …
Mobility Edge for L\'evy Matrices
A Aggarwal, C Bordenave, P Lopatto - arXiv preprint arXiv:2210.09458, 2022 - arxiv.org
L\'evy matrices are symmetric random matrices whose entry distributions lie in the domain of
attraction of an $\alpha $-stable law. For $\alpha< 1$, predictions from the physics literature …
attraction of an $\alpha $-stable law. For $\alpha< 1$, predictions from the physics literature …
Bernoulli random matrices
A Guionnet - arXiv preprint arXiv:2112.05506, 2021 - content.ems.press
Random matrix theory has become a field on its own with a breadth of new results,
techniques, and ideas in the last thirty years. In these proceedings, I illustrate some of these …
techniques, and ideas in the last thirty years. In these proceedings, I illustrate some of these …