On the genealogy of branching random walks and of directed polymers
arXiv:1607.06610 · doi:10.1209/0295-5075/115/40005
Abstract
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.
arXiv comment7 pages, 3 figures, submitted to EPL
References in corpus (20)
- Shape Fluctuations and Random Matrices
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- The one-dimensional KPZ equation: an exact solution and its universality
- Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
- An exact solution for the KPZ equation with flat initial conditions
- Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization
- A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
- A branching random walk seen from the tip
- Extreme Value Statistics of Hierarchically Correlated Variables: Deviation from Gumbel Statistics and Anomalous Persistence
- Statistics at the tip of a branching random walk and the delay of traveling waves
- Extreme Value Statistics and Traveling Fronts: An Application to Computer Science
- Turbo codes: the phase transition
- Traveling Waves, Front Selection, and Exact Nontrivial Exponents in a Random Fragmentation Problem
- Extremal Paths on a Random Cayley Tree
- Spatial Extent of Branching Brownian Motion
- Maximal displacement of a branching random walk in time-inhomogeneous environment
- Quantum chromodynamics at high energy and statistical physics
- Phenomenological picture of fluctuations in branching random walks
- Replica method and finite volume corrections
- Finite size corrections in the random energy model and the replica approach
Cited by in corpus (13)
- Liouville field theory and log-correlated Random Energy Models
- Diffractive electron-nucleus scattering and ancestry in branching random walks
- Rapidity gap distribution in diffractive deep-inelastic scattering and parton genealogy
- How to generate the tip of branching random walks evolved to large times
- One step replica symmetry breaking and extreme order statistics of logarithmic REMs
- Particle-number distribution in large fluctuations at the tip of branching random walks
- Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
- Nuclear scattering configurations of onia in different frames
- Darcy's law of yield stress fluids on a treelike network
- Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitions
- Replica-symmetry breaking for directed polymers
- Finite size corrections to the Parisi overlap function in the GREM
- Diffractive patterns in deep-inelastic scattering and parton genealogy