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              <p>This paper concerns the use of a particular class of determinantal point processes (DPP), a class of repulsive spatial point processes, for Monte Carlo integration.Let $d\ge 1$, $I\subseteq \overline d=\{1,\dots,d\}$ with $\iota=|I|$. Using a single set of $N$  quadrature points $\{u_1,\dots,u_N\}$ defined, once for all, in dimension $d$ from the realization of the DPP model, we investigate ``minimal'' assumptions on the integrand in order to obtain unbiased Monte Carlo estimates  of  $\mu(f_I)=\int_{[0,1]^\iota} f_I(u) \de u$  for any known $\iota$-dimensional integrable function on $[0,1]^\iota$. In particular, we show that the resulting estimator has variance with order $N^{-1-(2s\wedge 1)/d}$ when the integrand belongs to some Sobolev space with regularity $s &gt; 0$. When $s&gt;1/2$ (which includes a large class of non-differentiable functions), the variance is asymptotically explicit and the estimator is shown to satisfy a Central Limit Theorem.</p>
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