Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Optimal Exact Simulation of Max-Stable and Related Random Fields   We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log
A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$,
where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$
and $0<A_{1}<A_{2}<\cdots $ are the arrivals of a general renewal process on
$(0,\infty )$, independent of $(X_{n})$. In particular, a large class of
max-stable random fields with Gumbel marginals have such a representation.
Assume that one needs $c\left( d\right) =c(\{t_{1},\ldots,t_{d}\})$ function
evaluations to sample $X_{n}$ at $d$ locations $t_{1},\ldots ,t_{d}\in T$. We
provide an algorithm which, for any $\epsilon >0$, samples $M(t_{1}),\ldots
,M(t_{d})$ with complexity $o(c(d)\,d^{\epsilon })$. Moreover, if $X_{n}$ has
an a.s. converging series representation, then $M$ can be a.s. approximated
with error $\delta $ uniformly over $T$ and with complexity $O(1/(\delta \log
(1/\delta ))^{1/\alpha })$, where $\alpha $ relates to the H\"{o}lder
continuity exponent of the process $X_{n}$ (so, if $X_{n}$ is Brownian motion,
$\alpha =1/2$).

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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin