Self-interacting processes via Doob conditioning

Abstract

We connect self-interacting processes, that is, stochastic processes where transitions depend on the time spent by a trajectory in each configuration, to Doob conditioning. In this way we demonstrate that Markov processes with constrained occupation measures are realised optimally by self-interacting dynamics. We use a tensor network framework to guide our derivations. We illustrate our general results with new perspectives on well-known examples of self-interacting processes, such as random walk bridges, excursions, and forced excursions.

12 pages + References, 4 figures

References in corpus (36)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• The large deviation approach to statistical mechanics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A survey of random processes with reinforcement
• Nonequilibrium Markov processes conditioned on large deviations
• Large deviations and ensembles of trajectories in stochastic models
• Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Tensor Network Algorithms: a Route Map
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• On the time to reach maximum for a variety of constrained Brownian motions
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Effective dynamics of microorganisms that interact with their own trail
• Rare behavior of growth processes via umbrella sampling of trajectories
• A reinforcement learning approach to rare trajectory sampling
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Self Trapping of a Single Bacterium in its Own Chemoattractant
• Optimal non-Markovian search strategies with n-step memory
• Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Self-trapping self-repelling random walks
• Systematic derivation of hybrid coarse-grained models
• Application of importance sampling to the computation of large deviations in non-equilibrium processes
• Some particular self-interacting diffusions: Ergodic behaviour and almost sure convergence
• Non-reversible Monte Carlo: an example of 'true' self-repelling motion
• Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
• Adaptive power method for estimating large deviations in Markov chains
• Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• Chemical master equation parameter exploration using DMRG