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We constrain the $\Lambda$CDM cosmological parameter $\sigma_{8}$ by applyingthe extreme value statistics for galaxy cluster mass on the AMICO KiDS-DR3catalog. We sample the posterior distribution of the parameters by consideringthe likelihood of observing the largest cluster mass value in a sample of$N_{\textrm{obs}} = 3644$ clusters with intrinsic richness $\lambda^{*} > 20$in the redshift range $z\in[0.10, 0.60]$. We obtain$\sigma_{8}=0.90_{-0.18}^{+0.20}$, consistent within $1\sigma$ with themeasurements obtained by the Planck collaboration and with previous resultsfrom cluster cosmology exploiting AMICO KiDS-DR3. The constraints could improveby applying this method to forthcoming missions, such as $\textit{Euclid}$ andLSST, which are expected to deliver thousands of distant and massive clusters.

AMICO galaxy clusters in KiDS-DR3: constraints on $\Lambda$CDM from extreme value statistics