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math.PR2026
On the principal eigenvectors of random Markov matrices
Jacob Calvert, Frank den Hollander, Dana Randall
We analyze the invariant distributions of continuous-time and discrete-time random walks on randomly weighted complete digraphs. These distributions correspond to the principal lef…
math.PR2025
Local-global correlations of dynamics on disordered energy landscapes
Jacob Calvert, Dana Randall
The stationary distribution of a continuous-time Markov chain generally arises from a complicated global balance of probability fluxes. Nevertheless, empirical evidence shows that…
math.PR2024
A local-global principle for nonequilibrium steady states
Jacob Calvert, Dana Randall
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization bec…