Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodic properties of continuous-time random walks: finite-size effects
  and ensemble dependences   The effects of spatial confinements and smooth cutoffs of the waiting time
distribution in continuous-time random walks (CTRWs) are studied analytically.
We also investigate dependences of ergodic properties on initial ensembles
(i.e., distributions of the first waiting time). Here, we consider two
ensembles: the equilibrium and a typical non-equilibrium ensembles. For both
ensembles, it is shown that the time-averaged mean square displacement (TAMSD)
exhibits a crossover from normal to anomalous diffusion due to the spacial
confinement and this crossover does not vanish even in the long measurement
time limit. Moreover, for the non-equilibrium ensemble, we show that the
probability density function of the diffusion constant of TAMSD follows the
transient Mittag-Leffler distribution, and that scatter in the TAMSD shows a
clear transition from weak ergodicity breaking (an irreproducible regime) to
ordinary ergodic behavior (a reproducible regime) as the measurement time
increases. This convergence to ordinary ergodicity requires a long measurement
time compared to common distributions such as the exponential distribution; in
other words, the weak ergodicity breaking persists for a long time. In
addition, it is shown that, besides the TAMSD, a class of observables also
exhibits this slow convergence to ergodicity. We also point out that, even
though the system with the equilibrium initial ensemble shows no aging, its
behavior is quite similar to that for the non-equilibrium ensemble.

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The categories of this paper are: math-ph
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs