Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalable and Quasi-Contractive Markov Coupling of Maxwell Collision   This paper considers space homogenous Boltzmann kinetic equations in
dimension $d$ with Maxwell collisions (and without Grad's cut-off). An explicit
Markov coupling of the associated conservative (Nanbu) stochastic $N$-particle
system is constructed, using plain parallel coupling of isotropic random walks
on the sphere of two-body collisional directions. The resulting coupling is
almost surely decreasing, and the $L_2$-coupling creation is computed
explicitly. Some quasi-contractive and uniform in $N$ coupling / coupling
creation inequalities are then proved, relying on $2+\alpha$-moments ($\alpha
>0$) of velocity distributions; upon $N$-uniform propagation of moments of the
particle system, it yields a $N$-scalable $\alpha$-power law trend to
equilibrium. The latter are based on an original sharp inequality, which bounds
from above the coupling distance of two centered and normalized random
variables $(U,V)$ in $\R^d$, with the average square parallelogram area spanned
by $(U-U_\ast,V-V_\ast)$, $(U_\ast,V_\ast)$ denoting an independent copy. Two
counter-examples proving the necessity of the dependance on $>2$-moments and
the impossibility of strict contractivity are provided. The paper, (mostly)
self-contained, does not require any propagation of chaos property and uses
only elementary tools.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol