Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cutoff thermalization for Ornstein-Uhlenbeck systems with small L\'evy
  noise in the Wasserstein distance   This article establishes cutoff thermalization (also known as the cutoff
phenomenon) for a class of generalized Ornstein-Uhlenbeck systems
$(X^\varepsilon_t(x))_{t\geqslant 0}$ with $\varepsilon$-small additive L\'evy
noise and initial value $x$. The driving noise processes include Brownian
motion, $\alpha$-stable L\'evy flights, finite intensity compound Poisson
processes, and red noises, and may be highly degenerate. Window cutoff
thermalization is shown under mild generic assumptions; that is, we see an
asymptotically sharp $\infty/0$-collapse of the renormalized Wasserstein
distance from the current state to the equilibrium measure $\mu^\varepsilon$
along a time window centered on a precise $\varepsilon$- and $x$-dependent time
scale $t_\varepsilon^x$. In many interesting situations such as reversible
(L\'evy) diffusions it is possible to prove the existence of an explicit,
universal, deterministic cutoff thermalization profile. That is, for generic
initial data $x$ we obtain the stronger result
$\mathcal{W}_p(X^\varepsilon_{t_\varepsilon + r}(x), \mu^\varepsilon) \cdot
\varepsilon^{-1} \rightarrow K\cdot e^{-q r}$ as $\varepsilon \rightarrow 0$
for any $r\in \mathbb{R}$, some spectral constants $K, q>0$ and any $p\geqslant
1$ whenever the distance is finite. The existence of this limit is
characterized by the absence of non-normal growth patterns in terms of an
orthogonality condition on a computable family of generalized eigenvectors of
$\mathcal{Q}$. Precise error bounds are given. Using these results, this
article provides a complete discussion of the cutoff phenomenon for the
classical linear oscillator with friction subject to $\varepsilon$-small
Brownian motion or $\alpha$-stable L\'evy flights. Furthermore, we cover the
highly degenerate case of a linear chain of oscillators in a generalized heat
bath at low temperature.

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The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph