Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cusp of non-Gaussian density of particles for a diffusing diffusivity
  model   We study a two state ``jumping diffusivity'' model for a Brownian process
alternating between two different diffusion constants, $D_{+}>D_{-}$, with
random waiting times in both states whose distribution is rather general. In
the limit of long measurement times Gaussian behavior with an effective
diffusion coefficient is recovered. We show that for equilibrium initial
conditions and when the limit of the diffusion coefficient $D_-\to0$ is taken,
the short time behavior leads to a cusp, namely a non - analytical behavior, in
the distribution of the displacements $P(x,t)$ for $x\longrightarrow 0$.
Visually this cusp, or tent-like shape, resembles similar behavior found in
many experiments of diffusing particles in disordered environments, such as
glassy systems and intracellular media. This general result depends only on the
existence of finite mean values of the waiting times at the different states of
the model. Gaussian statistics in the long time limit is achieved due to
ergodicity and convergence of the distribution of the temporal occupation
fraction in state $D_{+}$ to a $\delta$-function. The short time behavior of
the same quantity converges to a uniform distribution, which leads to the non -
analyticity in $P(x,t)$. We demonstrate how super - statistical framework is a
zeroth order short time expansion of $P(x,t)$, in the number of transitions,
that does not yield the cusp like shape. The latter, considered as the key
feature of experiments in the field, is found with the first correction in
perturbation theory.

30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin