• The pervasive role of composition in machine learning (pdf)
  Notes from a talk at University of Oxford, July 2025
  
  
• On the heat kernel of a Cayley graph of PSL2(Z) (pdf)
  (with K. Kashaeva) arxiv preprint 2025
  
  
• Periodic approximation of topological Lyapunov exponents and the joint spectral radius for cocycles of mapping classes of surfaces (pdf)
  (with R. Mohammadpour) arxiv preprint 2025
  
  
• Training in reverse: How iteration order influences convergence and stability in deep learning (pdf)
  (with B. Dherin, B. Avelin, H. Mazzawi, J. Gonzalvo, M. Munn) arxiv preprint 2025
  
  
• The discrete analogue of the Gaussian (pdf)
  (with G. Chinta, J. Jorgenson and L. Smajlović) J. Physics A, 58 (2025) 035203 (22p)
  
  
• Torsion groups of subexponential growth cannot act on finite-dimensional CAT(0)-spaces without a fixed point (pdf)
  (with H. Izeki) To appear in Commentarii Math. Helv. (2025)
  
  
• Constructing heat kernels on infinite graphs (pdf)
  (with J. Jorgenson and L. Smajlović) Analysis and Applications (2025) 1-30
  
  
• The parametrix construction of the heat kernel on a graph (pdf)
  (with G. Chinta, J. Jorgenson and L. Smajlović) Complex Anal. Oper. Theory, 18 (2024) no. 8, 176
  
  
• The resolvent kernel on the discrete circle and twisted cosecant sums (pdf)
  (with J. Jorgenson and L. Smajlović) J. Math. Anal. Appl. 538 (2024) no. 2, 128454, 23 pp.
  
  
• The stars at infinity in several complex variables (pdf)
  Rendiconti Lincei Mat. Appl., 35 (2024) no. 1, 49-75
  
  
• A metric fixed point theorem and some of its applications (pdf)
  Geom. Funct. Anal. (GAFA) 34 (2024) 486-511 ( TheScienceBreaker)
  
  
• Backward dynamics of non-expanding maps of Gromov hyperbolic metric spaces (pdf)
  (with L. Arosio, M. Fiacchi, L. Guerini) Adv. Math. 439 (2024), 109484
  
  
• Generalized Lyapunov exponents and aspects of the theory of deep learning (pdf)
  In: New Trends in Lyapunov Exponents (Eds. Dias, Duarte, Gaivão, Klein, Peixe, Siqueira, Torres),
  CIM Ser. Math. Sci. Springer, 2023, pp. 99-118
  
  
• Volumes of spheres and special values of zeta functions of Z and Z/nZ (pdf)
  (with M. Pallich) Acta Arithmetica 208 (2023) 161-170.
  
  
• Deep limits and a cut-off phenomenon for neural networks (pdf)
  (with B. Avelin) Journal of Machine Learning Research 23 (191) (2022) 1-29. ( NeurIPS)
  
  
• Elements of a metric spectral theory (pdf)
  In: Dynamics, Geometry and Number Theory: the Impact of Margulis on Modern Mathematics
  The University of Chicago Press, 2022
  
  
• From linear to metric functional analysis (link)
  Proc Natl Acad Sci USA, July 13, 2021 118 (28) e2107069118
  
  
• Comments on the cosmic convergence of nonexpansive maps (pdf)
  (with A.W. Gutiérrez) Journal of Fixed Point Theory and Applications 23 (2021) 59
  
  
• A natural graph of finite fields distinguishing between models (pdf)
  (with G. Kuhn) Finite Fields Appl. 69 (2021) 101779
  
  
• Hahn-Banach for metric functionals and horofunctions (pdf)
  Journal of Functional Analysis 281:2 (2021) 109030
  
  
• Spectral zeta functions (pdf)
  In: Discrete and Continuous Models in the Theory of Networks (Eds. F.M. Atay, P.B. Kurasov, D. Mugnolo)
  Operator Theory: Advances and Appl. 281 (2020) Birkhauser, pp. 199-212
  
  
• Subadditive and multiplicative ergodic theorems (pdf)
  (with S. Gouëzel) J. Eur. Math. Soc. 22 (2020) 1893-1915
  
  
• A proof of the subadditive ergodic theorem (pdf)
  In: Groups, graphs and random walks (Eds. T. Ceccherini-Silberstein, M. Salvatori, E. Sava-Huss),
  London Math. Soc. Lecture Note Ser. 436 (2017) Cambridge Univ. Press pp. 343-354
  
  
• Spectral zeta functions of graphs and the Riemann zeta function in the critical strip (pdf)
  (with F. Friedli) Tohoku Math. J. (2) 69 (2017) 585-610.
  Graph L-functions and GRH (pdf) J. Number Theory F. Freidli.
  
  
• Dynamics of Hilbert nonexpansive maps (pdf)
  In: Handbook of Hilbert Geometry Ch. 9, pp 263-273, EMS, 2014
  
  
• Heat kernels on regular graphs and generalized Ihara zeta function formulas (pdf)
  (with G. Chinta and J. Jorgenson) Monatsh. Math. (2015) 178: 171-190
  
  
• Two extensions of Thurston's spectral theorem for surface diffeomorphisms (pdf)
  Bull. London Math. Soc. (2014) 46 (2): 217-226
  
  
• Complexity and heights of tori (pdf)
  (with G. Chinta and J. Jorgenson) In: Dynamical Systems and Group Actions
  (Eds. L. Bowen, R. Grigorchuk, Y. Vorobets),
  Contemporary Mathematics, 567 (2012) pp. 89-98
  
  
• Homomorphisms to R constructed from random walks (pdf)
  (with A. Erschler) Annales de l'institut Fourier 60 (2010) 2095-2113
  
  
• Noncommutative ergodic theorems (pdf)
  (with F. Ledrappier) In: Geometry, Rigidity and Group Actions (eds. Farb and Fisher),
  Chicago Lectures in Math, Chicago University Press, 2011, pp. 396-418
  
  
• Zeta functions, heat kernels and spectral invariants under degeneration of discrete tori (pdf)
  (with G. Chinta and J. Jorgenson) Nagoya Math. J. 198 (2010) 121-172
  
  
• Strong law of large numbers with concave moments (pdf)
  (with N. Monod) Not for publication.
  
  
• Ergodic theorems for noncommuting random products (pdf)
  Lecture notes from Santiago and Wroclaw.
  
  
• Applications of heat kernels on abelian groups:
  ζ(2n), quadratic reciprocity, Bessel integrals (pdf)
  In: Number theory, Analysis and Geometry. In memory of Serge Lang,
  (eds. Goldfeld, Jorgenson, Jones, Ramakrishnan, Ribet, Tate), Springer Verlag, 2012, pp 307-320
  
  
• Superrigidity, generalized harmonic maps, and uniformly convex spaces (pdf)
  (with T. Gelander and G.A. Margulis) GAFA. 17 (2008) 1524-1550
  
  
• Propriété de Liouville et vitesse de fuite du mouvement Brownien (preprint, scidirect)
  (with F. Ledrappier) C. R. Acad. Sci. Paris, Ser. I 344 (2007) 685-690
  
  
• Linear drift and Poisson boundary for random walks (pdf, PAMQ)
  (with F. Ledrappier) Pure Appl. Math. Q. 3 (2007) 1027-1036
  
  
• The Poisson boundary of Lamplighter random walks on trees (pdf, LINK)
  (with W. Woess) Geom. Dedicata, 124 (2007) 95-107
  
  
• Volumes of ideal simplices in Hilbert's geometry and symmetric spaces (pdf)
  (with M. Bucher-Karlsson) In: Guido's Book of Conjectures, I. Chatterji (ed.)
  l'Enseign. Math. (2008) pp. 53-55
  
  
• Heat kernels, theta identities, and zeta functions on cyclic groups (pdf)
  (with M. Neuhauser) In: Topological and Asymptotic Aspects of Group Theory,
  R. Grigorchuk, M. Mihalik, M. Sapir, Z. Sunik (eds.),
  Contemporary Mathematics, 394 (2006) pp. 177-189
  
  
• Laws of large numbers for random walks (pdf, aop)
  (with F. Ledrappier) Annals of Probability, 34 (2006) 1693-1706.
  
  
• Horoballs in simplices and Minkowski spaces (pdf)
  (with V. Metz and G. Noskov) Int. J. Math. Math. Sci. (2006) 20 pp.
  
  
• On the dynamics of isometries (pdf)
  Geometry & Topology, 9 (2005) 2359-2394.
  
  
• Hilbert metrics and Minkowski norms (pdf)
  (with T. Foertsch) Journal of Geometry, 83 (2005) 22-31.
  
  
• The Bass conjecture and growth in groups (pdf)
  (with M. Neuhauser) Colloq. Math. 100 (2004) 23-27.
  
  
• Some remarks concerning harmonic functions on homogeneous graphs (pdf)
  In: Discrete Random Walks, Cyril Banderier and Christian Krattenthaler (eds.),
  Discrete Mathematics and Theoretical Computer Science Proceedings AC, (2003) pp. 137-144
  
  
• Some groups having only elementary actions on metric spaces
  with hyperbolic boundaries (pdf)
  (with G. Noskov) Geom. Dedicata, 104 (2004) 119-137.
  
  
• Free subgroups of groups with nontrivial Floyd boundary (pdf)
  Comm. Algebra, 31 (2003) 5361-5376.
  
  
• On the definition of bolic spaces (pdf)
  (with M. Bucher) Expo. Math. 20 (2002) 269-277.
  
  
• Boundaries and random walks on finitely generated infinite groups (pdf, addendum)
  Arkiv för Matematik, 41 (2003) 295-306.
  
  
• Linear rate of escape and convergence in directions (pdf)
  In: Proceedings of a Workshop at the Schrödinger Institute, Vienna 2001,
  (Ed. by V.A. Kaimanovich, in collab. with K. Schmidt, W. Woess) de Gruyter, 2004.
  
  
• Hilbert's metric and Gromov hyperbolicity (pdf)
  (with G. Noskov) L'Enseign. Math. 48 (2002) 73-89.
  
  
• Nonexpanding maps, Busemann functions and Multiplicative ergodic theory (pdf)
  In: Proceedings of the Workshop in Ergodic theory, Geometric rigidity and Number theory,
  Newton Institute, Cambridge, (Eds. M. Burger and A. Iozzi) 283-294, Springer Verlag, 2002.
  
  
• Nonexpanding maps and Busemann functions (pdf)
  Erg. Th. & Dyn. Sys. 21 (2001) 1447-1457.
  
  
• An alternative proof of the subadditive ergodic theorem (pdf)
  Unpublished manuscript.
  
  
• A multiplicative ergodic theorem and nonpositively curved spaces (pdf)
  (with G. Margulis) Comm. Math. Phys. 208 (1999) 107-123.