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q-bio.PE2026
Extinction drives emergent metastability in complex ecosystems
Jong Il Park, Tim Rogers, Joseph W. Baron
Extinction is inevitable; every species eventually dies out, impacting the ecosystem it is part of. Over the past few decades, extensive research stemming from the stability-divers…
cond-mat.dis-nn2026
Lecture notes on random matrix theory: the results, the applications, and the analytical tools
Joseph W. Baron
Random matrix theory has established itself as a theoretical cornerstone of the mathematical sciences over the past century. It has undeniable utility in areas of research as diver…
cond-mat.dis-nn2026
Local density of states distribution and multifractal eigenvectors of weighted random networks via the cavity approach
Joseph W. Baron, Tim Rogers
We study the local density of states (LDoS) distribution of a general class of weighted Erdős-Rényi graphs. Using the cavity method, we obtain a good approximation to the full LDoS…