Giulio Tiozzo - Papers

Preprints

1. The Poisson boundary of discrete subgroups of semisimple Lie groups without moment conditions [PDF],
   with K. Chawla, B. Forghani, J. Frisch, arXiv:2509.02500.
2. Singularity of Furstenberg measure for infinite covolume discrete subroups in higher rank [PDF],
   with H. Lee, W. Van LimBeek, arXiv:2508.06329.
3. A cell decomposition for marked cycle curves [PDF],
   with C. Davis, M. Mukundan, D. Stoll, arXiv:2410.21049.
4. Metrics on trees I. The tower algorithm for interval maps [PDF],
   arXiv:2112.02398.

Published and accepted papers

5. The Poisson boundary of hyperbolic groups without moment conditions [PDF][Journal],
   with K. Chawla, B. Forghani, J. Frisch, Ann. Probab. 53 (2025), no. 5, 1897--1918.
6. Roots of Alexander polynomials of random positive 3-braids [PDF][Journal],
   with N. Dunfield, Adv. Math. 471 (2025), 110254.
7. Master Teapots and Entropy Algorithms for the Mandelbrot Set [PDF],
   with K. Lindsey, C. Wu, Trans. Amer. Math. Soc., 378 (2025), no. 5, 3297--3348. See also the Gallery.
8. A global shadow lemma and logarithm law for geometrically finite Hilbert geometries [PDF],
   with H. Bray, J. Mod. Dyn. 21 (2025), 443--496.
9. Genericity of contracting geodesics in groups [PDF],
   with K. Chawla, I. Choi, Groups Geom. Dyn. (2025), doi:10.4171/GGD/902.
10. Equidistribution of hyperbolic groups in homogeneous spaces [PDF] [Journal],
    with I. Gekhtman, S. Taylor, Math. Ann. 390 (2024), 4619--4638.
11. Sublinearly Morse Boundary II: Proper geodesic spaces [PDF],
    with Y. Qing, K. Rafi, Geom. Topol. 28 (2024), no. 4, 1829--1889.
12. A central limit theorem for the degree of a random product of Cremona transformations [PDF],
    with N.-B. Dang, Indiana Univ. Math. J. (2023) 72, no. 1, 301--329.
13. The core entropy for polynomials of higher degree [PDF] [Journal],
    with Y. Gao, J. Eur. Math. Soc. 24 (2022), no. 7, pp. 2555--2603.
14. The fundamental inequality for cocompact Fuchsian groups [PDF],
    with P. Kosenko, Forum of Math. Sigma 10 (2022), E102.
15. Central limit theorems for counting measures in coarse negative curvature [PDF] [slides] [video],
    with I. Gekhtman, S. Taylor, Compositio Math. 158 (2022), no. 10, 1980--2013.
16. Shannon's theorem for locally compact groups [PDF] [Journal] [slides],
    with B. Forghani, Ann. Probab. 50 (2022), no. 1, 61--89.
17. Appendix in Sublinearly Morse boundary I: CAT(0) spaces [PDF],
    by Y. Qing, K. Rafi, Adv. Math. 404 (2022), 108442.
18. Generalizations of Douady's magic formula [PDF] [Journal],
    with A. Epstein, Ergodic Theory Dynam. Systems 42 (2022), no. 9, 2784--2799.
19. The bifurcation locus for numbers of bounded type [PDF],
    with C. Carminati, Ergodic Theory Dynam. Systems 42 (2022), no. 7, 2239--2269.
20. Thermodynamic formalism for coarse expanding dynamical systems [PDF],
    with T. Das, F. Przytycki, M. rbański, A. Zdunik, Comm. Math. Phys. 384 (2021), 165--199.
21. Random walks, WPD actions, and the Cremona group [PDF] [Journal],
    with J. Maher, Proc. London Math. Soc. 123 (2021), no. 2, 153--202.
22. Cusp excursion in hyperbolic manifolds and singularity of harmonic measure [PDF],
    with A. Randecker, J. Mod. Dyn. 17 (2021), 183--211.
23. Excursions of generic geodesics in right-angled Artin groups and graph products [PDF],
    with Y. Qing, Int. Math. Res. Not. IMRN 2021 (2021), no. 22, 16910--16937.
24. Entropy and drift for Gibbs measures on geometrically finite manifolds [PDF],
    with I. Gekhtman, Trans. Amer. Math. Soc., 373 (2020), 2949--2980.
25. Counting problems in graphs products and relatively hyperbolic groups [PDF],
    with I. Gekhtman, S. Taylor, Israel J. Math. 237 (2020), 311--371.
26. Galois conjugates of entropies of real unimodal maps [PDF],
    Int. Math. Res. Not. IMRN 2020 (2020), no. 2, 607--640. See also the related Gallery.
27. A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture [PDF],
    with I. Gekhtman, S. Taylor, Adv. Math. 358 (2019), 106852.
28. Random walks of infinite moment on free semigroups [PDF],
    with B. Forghani, Probab. Theory Related Fields 175 (2019), no. 3, 1099--1122.
29. Random walks on weakly hyperbolic groups [PDF],
    with J. Maher, J. Reine Angew. Math. 742 (2018), 187--239.
30. Counting loxodromics for hyperbolic actions [PDF],
    with I. Gekhtman, S. Taylor, J. Topol. 11 (2018), no. 2, 379--419.
31. Continued fractions with SL(2, Z)-branches: combinatorics and entropy [PDF],
    with C. Carminati, S. Isola, Trans. Amer. Math. Soc. 370 (2018), no. 7, 4927--4973.
32. The local Hölder exponent for the entropy of real unimodal maps [PDF],
    Sci. China Math. (special issue dedicated to Tan Lei) 61 (2018), no. 12, 2299--2310.
33. Word length statistics for Teichmüller geodesics and singularity of harmonic measure [PDF],
    with V. Gadre, J. Maher, Comment. Math. Helv. 92 (2017), no. 1, 1--36.
34. Generalised continuation by means of right limits [PDF],
    with D. Sauzin, J. Anal. Math. 133 (2017), no. 1, 27--49.
35. The local Hölder exponent for the dimension of invariant subsets of the circle [PDF],
    with C. Carminati, Ergodic Theory Dynam. Systems 37 (2017), no. 6, 1825--1840.
36. Continuity of core entropy of quadratic polynomials [PDF] [Journal],
    Invent. Math. 203 (2016), no. 3, 891--921.
37. Random extensions of free groups and surface groups are hyperbolic [PDF],
    with S. Taylor, Int. Math. Res. Not. IMRN 2016 (2016), no. 1, 294--310.
38. Sublinear deviation between geodesics and sample paths [PDF],
    Duke Math. J. 164 (2015), no. 3, 511--539.
39. Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set [PDF],
    Adv. Math. 273 (2015), 651--715.
40. Word length statistics and Lyapunov exponents for Fuchsian groups with cusps [PDF],
    with V. Gadre, J. Maher, New York J. Math. 21 (2015), 511--531.
41. The entropy of Nakada's α-continued fractions: analytical results [PDF],
    Ann. Sc. Norm. Super. Pisa Cl. Sci. 13 (2014), 1009--1037.
42. Tuning and plateaux for the entropy of α-continued fractions [PDF],
    with C. Carminati, Nonlinearity 26 (2013), 1049--1070.
43. Dynamics of continued fractions and kneading sequences of unimodal maps [PDF],
    with C. Bonanno, C. Carminati, S. Isola, Discrete Contin. Dyn. Syst. 33 (2013), no. 4, 1313--1332.
44. A canonical thickening of Q and the entropy of α-continued fraction transformations [PDF],
    with C. Carminati, Ergodic Theory Dynam. Systems 32 (2012), no. 4, 1249--1269.
45. The entropy of α-continued fractions: numerical results [PDF],
    with C. Carminati, S. Marmi, A. Profeti, Nonlinearity 23 (2010), 2429--2456.