Fachbereich Mathematik

Arbeitsgruppe Stochastik

Schlossgartenstrasse 7

64289 Darmstadt

Germany

My research is in Probability and Statistical Mechanics. More specifically, I have acquired some experience with:

- Random walks, interacting particle systems (papers [3], [5] and [6])
- Self-avoiding walks, loop soups, spin systems (paper [1], [2], [4])
- Probabilistic cellular automata (papers [7] and [8])
- Mathematical models in epidemiology (paper [9])

- [1]:
*Shifted critical threshold in the loop O(n) model at arbitrarily small n.*

Lorenzo Taggi. ArXiv: 1806.09360 (2018). - [2]:
*Interacting self-avoiding polygons.*

Volker Betz, Helge Schäfer, Lorenzo Taggi. ArXiv: 1805.08517 (2018). - [3]:
*Active phase for activated random walks on Z*^{d}, d ≥ 3, with density less than one and arbitrary sleeping rate.

Lorenzo Taggi. ArXiv: 1712.05292 (2017). - [4]:
*Scaling limit of a self-avoiding walk interacting with spatial random permutations.*Volker Betz and Lorenzo Taggi. Submitted. ArXiv: 1612.07234 (2016).

- [5]:
*Critical density of activated random walks on Z*^{d}and general graphs.

Alexandre Stauffer and Lorenzo Taggi. Annals of Probability, Vol 46, No 4, Pag 2190-2220. ArXiv: 1512.02397 (2015). - [6]:
*Absorbing-state phase transition in biased Activated Random Walk.*Lorenzo Taggi. Electronic Journal of Probability, Volume 21, Issue 13, (2016). ArXiv: 1403.1986 (2014).

- [7]:
*Convergence Time of Probabilistic Cellular Automata.*Lorenzo Taggi. Book chapter on Probabilistic Cellular Automata - Theory, Applications and Future Perspectives (editors: Francesca Nardi and Pierre-Yves Louis, Springer) (2018).

- [8]:
*Critical Probabilities and Convergence Time of Percolation Probabilistic Cellular Automata.*

Lorenzo Taggi. Journal of Statistical Physics: Volume 159, Issue 4 (2015), Page 853-892. ArXiv: 1312.6990 (2014). - [9]:
*Dynamical correlations in the Escape Strategy of Influenza A virus,*

L. Taggi, F. Colaiori, V. Loreto, F. Tria.*Europhysics Letters*- 101, 68003 (2013). ArXiv: 1305.3418 (2013). -
*Size and structure of an epistatic space.*

L. Taggi, F. Colaiori, V. Loreto, F. Tria. Supplementary information to [5] (non intended for publication). ArXiv: 1303.5953 (2013).

I offered two courses for master students in mathematics at TU Darmstadt.

The course studies recurrence properties of random walks on general graphs. The analysis is carried on by introducing potential theory and the mathematical formalism of electric networks.

**Literature: ** Probability on Trees and Networks, by Lyons and Peres. Intesection of Random Walks, by G. F. Lawler.

The course explores the properties of spin systems with discrete and continuous symmetries. The program includes existence of the thermodynamic limit, high and low temperature representation for the Ising model, correlation inequalities, Lee and Yang cirle theorem, Mermin-Wagner theorem and connections to random walks.

**Literature: ** Statistical Mechanics of Lattice Systems a Concrete Mathematical Introduction, of S. Friedly and Y. Velenik

- Spring school Geometric Models in Probability (TU Darmstadt, April 2016)
- Rhein-Main Kolloquium (Darmstadt, Mainz, Frankfurt)
- Probability Oberseminar at TU-Darmstadt
- School and Workshop on Random Interacting System (University of Bath, June 2016)
- Stochastic and Analytic Methods in Mathematical Physics (Yerevan, Armenia, September 2016)
- Statistical Mechanics, random planar geometry and interacting random walks (Lyon, France, June 2017)
- First Italian meeting of probability and mathematical statistics (Torino, Italy, June 2017)
- University of Warwick (November, 2017)
- Workshop "Random strongly interacting systems" (Oberwolfach, January 2018)
- University of Warwick (November, 2017)
- Workshop on probabilistic approaches to quantum spin systems (Gothenburg, April 2018)

- (July 2018- January 2019) Post-Doc visitor at University of Bath (EPSRC grant).
- (2015-present) Post-Doc Fellow at TU Darmstadt (DFG grant).
- (2011-2015) Ph.D. in Mathematics at Max Planck Institute for Mathematics in the Sciences. Supervisor: Artem Sapozhnikov.
- (2008-2010) Master in Statistical Physics at Sapienza Università di Roma. Supervisor: Vittorio Loreto.
- (2005-2008) Bachelor in Physics at Sapienza Università di Roma. Supervisor: Miguel Virasoro.

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