Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConvergence of symmetric trap models in the hypercube
190
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider symmetric trap models in the d-dimensional hypercube whose ordered mean waiting times, seen as weights of a measure in the natural numbers, converge to a finite measure as d diverges, and show that the models suitably represented converge to a K process as d diverges. We then apply this result to get K processes as the scaling limits of the REM-like trap model and the Random Hopping Times dynamics for the Random Energy Model in the hypercube in time scales corresponding to the ergodic regime for these dynamics.
rate research
Read More
We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are unique viscosity solutions of first- or second-order partial differential equations depending on whether the growth models are scaled hyperbolically or parabolically. The results simplify and extend a recent work by the first author to more general surface growth models. The proofs are based on the methodology developed by Barles and the second author to prove convergence of approximation schemes.
We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape. We apply this proof to aging for trap models on large two-dimensional tori and for trap dynamics of the Random Energy Model on a broad range of time scales.
We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L{e}vy processes by using harmonic function and reversible measure. As direct applications, explicit sufficient conditions for exponential and strong ergodicity are given. Some examples are also presented.
We give the ``quenched scaling limit of Bouchauds trap model in ${dge 2}$. This scaling limit is the fractional-kinetics process, that is the time change of a $d$-dimensional Brownian motion by the inverse of an independent $alpha$-stable subordinator.
We discuss the long term behaviour of trap models on the integers with asymptotically vanishing drift, providing scaling limit theorems and ageing results. Depending on the tail behaviour of the traps and the strength of the drift, we identify three different regimes, one of which features a previously unobserved limit process.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
