Dynamic polymers: invariant measures and ordering by noise

@article{Bakhtin2021DynamicPI,
  title={Dynamic polymers: invariant measures and ordering by noise},
  author={Yuri Bakhtin and Hong-Bin Chen},
  journal={Probability Theory and Related Fields},
  year={2021}
}
We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic nearest neighbor interaction and local interaction with random environment. We prove existence and uniqueness of the solution, continuity of the flow, the order-preserving property with respect to the coordinatewise partial order, and the invariance of the… 
1 Citations
Invariant measures for stochastic conservation laws on the line
We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We

References

SHOWING 1-10 OF 71 REFERENCES
Localization and Perron--Frobenius theory for directed polymers
We consider directed polymers in a random potential given by a deterministic profile with a strong maximum at the origin taken with random sign at each integer time. We study two main objects based
BUSEMANN FUNCTIONS AND GIBBS MEASURES IN DIRECTED POLYMER MODELS ON Z2 BY CHRISTOPHER JANJIGIAN*
We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the
The endpoint distribution of directed polymers
Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we
Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation
The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and space‐continuous polymer model of a random walk in a random potential. These results include: existence of
Localization of directed polymers in continuous space
The first main goal of this article is to give a new metrization of the Mukherjee--Varadhan topology, recently introduced as a translation-invariant compactification of the space of probability
Ratios of partition functions for the log-gamma polymer
We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition in-
Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models
We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting
Attractor Properties for Irreversible and Reversible Interacting Particle Systems
We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be
Geometry of geodesics through Busemann measures in directed last-passage percolation
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of
Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation
We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we
...
...