Berlin 2015 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 33: Critical Phenomena and Phase Transitions
DY 33.3: Talk
Wednesday, March 18, 2015, 15:30–15:45, BH-N 334
To return or not to return? Phase transition to transience and congestion in random walks and queueing systems — •Andreas Sorge1,2,4, Jan Nagler3,4, Stephan Herminghaus1,2, and Marc Timme1,2,4 — 1MPI for Dynamics and Self-Organization, Göttingen, Germany — 2Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Germany — 3Computational Physics, IfB, ETH Zürich, Switzerland — 4Organization for Research on Complex Adaptive Systems (or-cas), Göttingen, Germany
Will a random walker ever return to where she started, and keep returning forever? When we are unaware of the law governing the walk, wisdom has it that we cannot infer recurrence from a finite-time sample trajectory. In 1890, Henri Poincaré introduced the very idea of such recurrences as a stability criterion. This criterion also applies to stochastic dynamical systems: By tuning the system parameter, a random walk loses recurrence and becomes unstable at a critical point. Intriguingly, this constitutes a phase transition to transience in Markovian systems. Here, we present a practical method to determine the critical point and the critical exponents of such systems in Monte-Carlo simulations. We also introduce the freely available Python implementation for effective and reproducible use of our method. Our findings and tools may be helpful in computational studies of stochastic systems, in particular queueing systems and dynamical congestion phenomena.