Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

RDA for Data Management Planning Community Cross-fertilisation Workshop Summary

The community cross-fertilisation workshop, ‘RDA for Data Management Planning’, brought chairs and members of RDA Working Groups (WGs) and Interest Groups (IGs) together, with members of the wider research data community, to share and discuss challenges, solutions and initiatives associated with data management plans (DMPs). The key findings of the workshop summarised herein will be used to direct the future strategy of the RDA community. Read more about the community cross-fertilisation workshop series in commemoration of the RDA’s 10th Anniversary