Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Survival probability of stochastic processes beyond persistence
  exponents   For many stochastic processes, the probability $S(t)$ of not-having reached a
target in unbounded space up to time $t$ follows a slow algebraic decay at long
times, $S(t)\sim S_0/t^\theta$. This is typically the case of symmetric compact
(i.e. recurrent) random walks. While the persistence exponent $\theta$ has been
studied at length, the prefactor $S_0$, which is quantitatively essential,
remains poorly characterized, especially for non-Markovian processes. Here we
derive explicit expressions for $S_0$ for a compact random walk in unbounded
space by establishing an analytic relation with the mean first-passage time of
the same random walk in a large confining volume. Our analytical results for
$S_0$ are in good agreement with numerical simulations, even for strongly
correlated processes such as Fractional Brownian Motion, and thus provide a
refined understanding of the statistics of longest first-passage events in
unbounded space.

16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio