I am currently a Hausdorff postdoc in the group of Prof. Juan J.L. Velazquez. I did my PhD at the Max Planck Institute for Mathematics in the Sciences of Leipzig under the supervision of Prof. Felix Otto.
My research lies in the fields of analysis of PDEs and probability. I am especially interested in
- Stochastic homogenization for elliptic operators
- Random walks in random environments and interacting particles systems
- Fluid flows in porous media
- Magnetic Schroedinger operators
P. Bella, A. Giunti and F. Otto, Quantitative stochastic homogenization: Control of local homogenization error through corrector, in Mathematics and Materials, Park City Mathematics series, pp. 299-327, 2015;
J. Conlon, A.Giunti and F.Otto, Green's function for elliptic systems: Existence and Delmotte-Deuschel bounds, in Calc.Var. and PDEs, Vol.56 n.6, 2017;
A. Giunti and J.-C. Mourrat, Quantitative homogenization of degenerate random environments, in Ann. Inst. H. Poincare' Probab. Statist., Vol.54 n.1, pp.22-50, 2018;
P. Bella and A. Giunti, Green's function for elliptic systems: Moment bounds, in Net. and Het. Media, Vol.13 n.1, pp.155-176, 2018;
A. Giunti, Y.Gu and J.-C. Mourrat, Heat kernel upper bounds for interacting particle systems, in Annals of Prob., 47(2): 1056-1095, 2019;
A. Giunti, R.M. Hoefer and J.J.L. Velazquez, Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes, in Comm. in PDEs, 43(9): 1377-1412, 2018;
A. Giunti and R.M. Hoefer, Homogenization for the Stokes equations in randomly perforated domains under almost minimal assumptions on the size of the holes, in Ann. Inst. H. Poincare'- An. Nonl., 36(7): 1829-1868, 2019;
A. Giunti and J.J.L. Velazquez, On the homogenization of random stationary elliptic operators in divergence form, to appear in Proc. of AMS, arXiv preprint 1809.06111;
P. Bella, A. Giunti and F. Otto, Effective multipoles in random media, to appear in Comm. PDEs, ArXiv preprint 1708.07672;
A. Giunti and F. Otto, On the existence of the Green function for elliptic systems in divergence form, ArXiv preprint 1911.02110;
- A. Giunti and J.J.L. Velazquez, Edge states for the magnetic Laplacian in domains with smooth boundary, ArXiv preprint 1912.07261;
A. Giunti and R.M. Hoefer, Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains, ArXiv preprint 2003.04724.
A. Giunti, Convergence rates for the homogenization of the Poisson problem in randomly perforated domains, ArXiv preprint 2007.13386.