Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trajectory-to-trajectory fluctuations in first-passage phenomena in
  bounded domains   We study the statistics of the first passage of a random walker to absorbing
subsets of the boundary of compact domains in different spatial dimensions. We
describe a novel diagnostic method to quantify the trajectory-to-trajectory
fluctuations of the first passage, based on the distribution of the so-called
uniformity index $\omega$, measuring the similarity of the first passage times
of two independent walkers starting at the same location. We show that the
characteristic shape of $P(\omega)$ exhibits a transition from unimodal to
bimodal, depending on the starting point of the trajectories. From the study of
different geometries in one, two and three dimensions, we conclude that this
transition is a generic property of first passage phenomena in bounded domains.
Our results show that, in general, the Mean First Passage Time (MFPT) is a
meaningful characteristic measure of the first passage behaviour only when the
Brownian walkers start sufficiently far from the absorbing boundary.
Strikingly, in the opposite case, the first passage statistics exhibit large
trajectory-to-trajectory fluctuations and the MFPT is not representative of the
actual behaviour.

32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess