Legged robots that operate in the real world are inherently subject to stochasticity in their
dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited …

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In this paper we continue the investigation of the spectral theory and exponential
asymptotics of primarily discrete-time Markov processes, following Kontoyiannis and Meyn …

Finite Markov chains, memoryless random walks on complex networks, appear commonly
as models for stochastic dynamics in condensed matter physics, biophysics, ecology …

Metastable states in stochastic systems are often characterized by the presence of small
eigenvalues in the generator of the stochastic dynamics. We here show that metastability in …

We describe state-reduction algorithms for the analysis of first-passage processes in
discrete-and continuous-time finite Markov chains. We present a formulation of the graph …

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful
mathematical way to approach this phenomenon is the study of rare transitions Markov …

Markov chains can accurately model the state-to-state dynamics of a wide range of complex
systems, but the underlying transition matrix is ill-conditioned when the dynamics feature a …

We consider the Kuramoto model of coupled oscillators with nearest-neighbour coupling
and additive white noise. We show that synchronous solutions which are stable without the …

We study the hitting times of Markov processes to target set G, starting from a reference
configuration x_0 or its basin of attraction. The configuration x_0 can correspond to the …