Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-performance of sharp restart I: Statistical roadmap   Restart is a general framework, of prime importance and wide applicability,
for expediting first-passage times and completion times of general stochastic
processes. Restart protocols can use either deterministic or stochastic timers.
Restart protocols with deterministic timers -- "sharp restart" -- assume a
principal role: if there exists a restart protocol that improves
mean-performance, then there exists a sharp-restart protocol that performs as
good or better. This paper, the first of a duo, presents a comprehensive
mean-performance analysis of sharp restart. Using statistical methods, the
analysis establishes universal criteria that determine when sharp restart
improves or worsens mean-performance, i.e., decreases or increases mean
first-passage/completion times. These criteria are akin to those recently
discovered for the most widely applied restart protocols -- "exponential
restart" -- which use exponentially-distributed timers. However, while the
exponential-restart criteria cover only the case of slow timers, the
sharp-restart criteria established here further cover the cases of fast,
critical, and general timers; moreover, the latter criteria address the very
existence of timers with which sharp restart improves or worsens
mean-performance. Using the slow-timers criteria, we discover a general
scenario for which: sharp restart improves mean-performance, whereas
exponential restart worsens mean-performance. The potency of the novel results
presented here is demonstrated by examples, and by the results' application to
canonical diffusion processes.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con