Concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. (arXiv:2011.11435v4 [math.PR] UPDATED)

We prove a new concentration inequality for U-statistics of order two for
uniformly ergodic Markov chains. Working with bounded and $\pi$-canonical
kernels, we show that we can recover the convergence rate of Arcones and
Gin{\'e} who proved a concentration result for U-statistics of independent
random variables and canonical kernels. Our result allows for a dependence of
the kernels $h_{i,j}$ with the indexes in the sums, which prevents the use of
standard blocking tools. Our proof relies on an inductive analysis …

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