Delocalization Transition for Critical Erdős–Rényi Graphs

Autor: Johannes Alt, Raphael Ducatez, Antti Knowles

Publikováno v: Communications in Mathematical Physics

We analyse the eigenvectors of the adjacency matrix of a critical Erdős–Rényi graph $${\mathbb {G}}(N,d/N)$$ G ( N , d / N ) , where d is of order $$\log N$$ log N . We show that its spectrum splits into two phases: a delocalized phase in the mid

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c241118398aa0409f19b930eeb7baa08
http://europepmc.org/articles/PMC8550299

Extremal eigenvalues of critical Erdős–Rényi graphs

Autor: Raphael Ducatez, Johannes Alt, Antti Knowles

Publikováno v: The Annals of Probability. 49

We complete the analysis of the extremal eigenvalues of the adjacency matrix A of the Erdős–Renyi graph G(N,d/N) in the critical regime d≍logN of the transition uncovered in (Ann. Inst. Henri Poincare Probab. Stat. 56 (2020) 2141–2161; Ann. Pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0c04b1a96bf92b75d3790a4c38a5182f
https://doi.org/10.1214/20-aop1483

Inhomogeneous Circular Law for Correlated Matrices

Autor: Johannes Alt, Torben Krüger

Publikováno v: Journal of Functional Analysis
Alt, J & Krüger, T 2021, ' Inhomogeneous circular law for correlated matrices ', Journal of Functional Analysis, vol. 281, no. 7, 109120 . https://doi.org/10.1016/j.jfa.2021.109120

We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density, expressed in terms

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0a98cfdf43a02fc26fe96942259eedd

Local inhomogeneous circular law

Autor: Torben Krüger, Johannes Alt, Laszlo Erdos

Publikováno v: Ann. Appl. Probab. 28, no. 1 (2018), 148-203

We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b34e64ca50ad74cb1aa3b53687044b8
https://doi.org/10.1214/17-aap1302

Singularities of the density of states of random Gram matrices

Autor: Johannes Alt

Publikováno v: Electron. Commun. Probab.

For large random matrices $X$ with independent, centered entries but not necessarily identical variances, the eigenvalue density of $XX^*$ is well-approximated by a deterministic measure on $\mathbb{R}$. We show that the density of this measure has o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::af1e43165cd6ba0b93966b3870259dd1
http://arxiv.org/abs/1708.08442