Delocalization-localization dynamical phase transition of random walks on graphs

Abstract

We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order dynamical phase transition (DPT). This is interpreted as a `co-existence' of paths in the fluctuations that visit the highly connected bulk of the graph (delocalization) and paths that visit the boundary (localization). The methods we used also allow us to characterize analytically the scaling function that describes the finite size crossover between the localized and delocalized regimes. Remarkably, we also show that the DPT is robust with respect to a change in the graph topology, which only plays a role in the crossover regime. All results support the view that a first-order DPT may also appear in random walks on infinite-size random graphs.

arXiv comment12 pages, 6 figures

References in corpus (23)

• Statistical physics of social dynamics
• Epidemic processes in complex networks
• The large deviation approach to statistical mechanics
• Random walks and diffusion on networks
• Nonequilibrium Markov processes conditioned on large deviations
• Introduction to dynamical large deviations of Markov processes
• Variational and optimal control representations of conditioned and driven processes
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Extreme events on complex networks
• Level 2 large deviation functionals for systems with and without detailed balance
• Controlling the uncertain response of real multiplex networks to random damage
• Large deviations of random walks on random graphs
• Finite time large deviations via matrix product states
• Large deviations in the presence of cooperativity and slow dynamics
• Role of current fluctuations in nonreversible samplers
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Graph-combinatorial approach for large deviations of Markov chains
• Varied phenomenology of models displaying dynamical large-deviation singularities
• BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Reactive explorers to unravel network topology
• Maximal dispersion of adaptive random walks
• Random Walks on Complex Networks

Cited by in corpus (8)

• Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• Adaptive power method for estimating large deviations in Markov chains
• Dynamical fluctuations of random walks in higher-order networks
• Convergence of the Integral Fluctuation Theorem estimator for nonequilibrium Markov systems
• Bringing together two paradigms of non-equilibrium: Fragile versus robust aging in driven glassy systems
• Understanding random-walk dynamical phase coexistence through waiting times
• Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion