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    Homogenization in random Dirichlet forms

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    A general diffusion process in a random medium associated with a random Dirichlet form with nonsmooth and nonbounded coefficients is considered, as drift transformation of a starting diffusion process in a random medium, with random infinitesimal generator in divergence form. The corresponding homogenization problem is studied and conditions are found such that the suitably rescaled original process converges weakly, as the scaling parameter is sent to the limit, to a diffusion process with constant coefficients. Stochastic analysis associated with Dirichlet forms is used in the proof

    Distributed Lag Non-Linear Models for the impact of heat waves on elderly people living in the regions of central-eastern Italy

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    Background: Prolonged periods of extreme heat, usually referred to as heat waves, have a significant impact on health, especially in the most vulnerable populations. In the present study, we investigated the effect of heat waves on mortality in the elderly population living in the regions of central-eastern Italy. Methods: We considered 10 cities located between the Marche and Abruzzo regions during the period 2011-2021. The association between heat waves and mortality risk was analysed for each city using nonlinear distributed lag temperature and humidity functions, a method that accounts for nonlinear lagged effects, including the short- and medium-term harvest effect. We then performed a multivariate meta-analysis on all cities to jointly synthesise multiple results on mortality risk during heat waves, taking into account their correlation. Results: In the first days after the heat wave, the relative risk (RR) tends to increase, then decreases with a lag of about 4 days and then stabilises around the reference value (RR = 1), with a slight increase around day 21-22. Conclusion: The study shows a significant increase in risk in the presence or after the occurrence of a heat wave. The heterogeneous behaviour of some cities (e.g. San Benedetto del Tronto) could be due to other factors (e.g. pollution) that need to be investigated. The aggregate analysis allows a more robust estimate of the overall effect, reducing the uncertainty arising from individual local analyses

    On the role of the central limit theorem in 3d quantum gravity

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    Based on a combinatorial approach to quantum gravity and random matrix theory, we show a central limit theorem that gives important insight into causally triangulated 3D quantum gravity
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