Ergodicity coefficients for higher-order stochastic processes
SIAM Journal on Mathematics of Data Science, vol. 2, pp. 740–769, 2020
The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in numerous application settings. In many cases of practical interest, these processes …
The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms
Journal of Scientific Computing, vol. 88, pp. 21, 2021
We analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate $\ell^p$ matrix norms. In particular, …
Nonlocal PageRank
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, pp. 77–97, 2021
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not …