6 papers
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…
Correlation thresholds in the steady states of particle systems and spin glasses
Jacob Calvert, Dana Randall
A growing body of theoretical and empirical evidence shows that the global steady-state distributions of many equilibrium and nonequilibrium systems approximately satisfy an analog…
How many more is different?
Jacob Calvert, Andréa W. Richa, Dana Randall
From the formation of ice in small clusters of water molecules to the mass raids of army ant colonies, the emergent behavior of collectives depends critically on their size. At the…
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…
The Geometry of Fixed-Magnetization Spin Systems at Low Temperature
Jacob Calvert, Shunhao Oh, Dana Randall
Spin systems are fundamental models of statistical physics that provide insight into collective behavior across scientific domains. Their interest to computer science stems in part…
Single Bridge Formation in Self-Organizing Particle Systems
Shunhao Oh, Joseph Briones, Jacob Calvert +3
Local interactions of uncoordinated individuals produce the collective behaviors of many biological systems, inspiring much of the current research in programmable matter. A striki…