• Download PDF
• Download TeX
• Download bibTeX entry

Metadata

Abstract

References

[ABB + 17] Abert, Miklos; Bergeron, Nicolas; Biringer, Ian; Gelander, Tsachik; Nikolov, Nikolay; Raimbault, Jean; Samet, Iddo On the growth of $L^2$-invariants for sequences of lattices in Lie groups, Ann. Math., Volume 185 (2017) no. 3, pp. 711-790 | DOI | MR | Zbl

[ABBG23] Abért, Miklós; Bergeron, Nicolas; Biringer, Ian; Gelander, Tsachik Convergence of normalized Betti numbers in nonpositive curvature, Duke Math. J., Volume 172 (2023) no. 4, pp. 633-700 | DOI | MR | Zbl

[AGG89] Arratia, Richard A.; Goldstein, Larry; Gordon, Louis Two moments suffice for Poisson approximations: the Chen–Stein method, Ann. Probab., Volume 17 (1989) no. 1, pp. 9-25 | MR | Zbl

[Ago13] Agol, Ian The virtual Haken conjecture, Doc. Math., Volume 18 (2013), pp. 1045-1087 (with an appendix by Agol, Daniel Groves, and Jason Manning) | MR | Zbl

[AGV14] Abért, Miklós; Glasner, Yair; Virág, Bálint Kesten’s theorem for invariant random subgroups, Duke Math. J., Volume 163 (2014) no. 3, pp. 465-488 | DOI | MR | Zbl

[AL02] Amit, Alon; Linial, Nathan Random graph coverings. I. General theory and graph connectivity, Combinatorica, Volume 22 (2002) no. 1, pp. 1-18 | DOI | MR | Zbl

[BBG + 18] Baik, Hyungryul; Bauer, David; Gekhtman, Ilya; Hamenstädt, Ursula; Hensel, Sebastian; Kastenholz, Thorben; Petri, Bram; Valenzuela, Daniel Exponential torsion growth for random 3-manifolds, Int. Math. Res. Not., Volume 21 (2018), pp. 6497-6534 | DOI | MR | Zbl

[BCP19] Budzinski, Thomas; Curien, Nicolas; Petri, Bram Universality for random surfaces in unconstrained genus, Electron. J. Comb., Volume 26 (2019) no. 4, 4.2 | DOI | MR | Zbl

[BG04] Bergeron, Nicolas; Gaboriau, Damien Asymptotique des nombres de Betti, invariants $l^2$ et laminations, Comment. Math. Helv., Volume 79 (2004) no. 2, pp. 362-395 | DOI | MR | Zbl

[BG07] Benaych-Georges, Florent Cycles of random permutations with restricted cycle lengths (2007) (https://arxiv.org/abs/0712.1903v1)

[BG10] Benaych-Georges, Florent Cycles of free words in several independent random permutations with restricted cycle lengths, Indiana Univ. Math. J., Volume 59 (2010) no. 5, pp. 1547-1586 | DOI | MR | Zbl

[BHJ92] Barbour, Andrew D.; Holst, Lars; Janson, Svante Poisson approximation, Oxford Studies in Probability, 2, Clarendon Press, 1992 (Oxford Science Publications) | DOI | MR | Zbl

[BKL + 20] Baader, Sebastian; Kjuchukova, Alexandra; Lewark, Lukas; Misev, Filip; Ray, Arunima Average four-genus of two-bridge knots (2020) (https://arxiv.org/abs/1902.05721, to appear in Proceedings of the American Mathematical Society)

[BM04] Brooks, Robert; Makover, Eran Random construction of Riemann surfaces, J. Differ. Geom., Volume 68 (2004) no. 1, pp. 121-157 | MR | Zbl

[Bol80] Bollobás, Béla A probabilistic proof of an asymptotic formula for the number of labelled regular graphs, Eur. J. Comb., Volume 1 (1980) no. 4, pp. 311-316 | DOI | MR | Zbl

[Bol85] Bollobás, Béla Random graphs, Academic Press Inc., 1985 | MR | Zbl

[Bow14] Bowen, Lewis Random walks on random coset spaces with applications to Furstenberg entropy, Invent. Math., Volume 196 (2014) no. 2, pp. 485-510 | DOI | MR | Zbl

[BPR20] Baik, Hyungryul; Petri, Bram; Raimbault, Jean Subgroup growth of right-angled Artin and Coxeter groups, J. Lond. Math. Soc., II. Ser., Volume 101 (2020) no. 2, pp. 556-588 | DOI | MR | Zbl

[BS01] Benjamini, Itai; Schramm, Oded Recurrence of distributional limits of finite planar graphs, Electron. J. Probab., Volume 6 (2001), no. 23 | DOI | MR | Zbl

[CGS11] Chen, Louis H. Y.; Goldstein, Larry; Shao, Qi-Man Normal approximation by Stein’s method, Probability and Its Applications, Springer, 2011 | DOI | MR | Zbl

[CHM51] Chowla, Sarvadaman; Herstein, Israel N.; Moore, W. K. On recursions connected with symmetric groups. I, Can. J. Math., Volume 3 (1951), pp. 328-334 | DOI | MR | Zbl

[CMZ18] Chen, Dawei; Möller, Martin; Zagier, Don Quasimodularity and large genus limits of Siegel–Veech constants, J. Am. Math. Soc., Volume 31 (2018) no. 4, pp. 1059-1163 | DOI | MR | Zbl

[Dix69] Dixon, John D. The probability of generating the symmetric group, Math. Z., Volume 110 (1969), pp. 199-205 | DOI | MR | Zbl

[DJPP13] Dumitriu, Ioana; Johnson, Tobias; Pal, Soumik; Paquette, Elliot Functional limit theorems for random regular graphs, Probab. Theory Relat. Fields, Volume 156 (2013) no. 3-4, pp. 921-975 | DOI | MR | Zbl

[DT06] Dunfield, Nathan M.; Thurston, William P. Finite covers of random 3-manifolds, Invent. Math., Volume 166 (2006) no. 3, pp. 457-521 | DOI | MR | Zbl

[Eck04] Eckmann, Beno Lattices, $l_2$-Betti numbers, deficiency, and knot groups, Enseign. Math., Volume 50 (2004) no. 1-2, pp. 123-137 | MR | Zbl

[Ele10] Elek, Gábor Betti numbers are testable, Fete of combinatorics and computer science (Bolyai Society Mathematical Studies), Volume 20, János Bolyai Mathematical Society, 2010, pp. 139-149 | DOI | MR | Zbl

[EZ17] Even-Zohar, Chaim Models of random knots, J. Appl. Comput. Topol., Volume 1 (2017) no. 2, pp. 263-296 | DOI | MR | Zbl

[FPP + 21] Friedl, S.; Park, J.; Petri, B.; Raimbault, Jean; Ray, A. On distinct finite covers of 3-manifolds, Indiana Univ. Math. J., Volume 70 (2021) no. 2, pp. 809-846 | DOI | MR | Zbl

[Fri08] Friedman, Joel A proof of Alon’s second eigenvalue conjecture and related problems, Memoirs of the American Mathematical Society, 910, American Mathematical Society, 2008 | DOI | MR | Zbl

[Gel18] Gelander, Tsachik A lecture on invariant random subgroups, New Directions in Locally Compact Groups, Cambridge University Press, 2018, pp. 186-204 | DOI | MR | Zbl

[GJKW02] Greenhill, Catherine; Janson, Svante; Kim, Jeong Han; Wormald, Nicholas C. Permutation pseudographs and contiguity, Comb. Probab. Comput., Volume 11 (2002) no. 3, pp. 273-298 | DOI | MR | Zbl

[GLMST21] Gilmore, Clifford; Le Masson, Etienne; Sahlsten, Tuomas; Thomas, Joe Short geodesic loops and $L^p$ norms of eigenfunctions on large genus random surfaces, Geom. Funct. Anal., Volume 31 (2021) no. 1, pp. 62-110 | DOI | MR | Zbl

[GPY11] Guth, Larry; Parlier, Hugo; Young, Robert Pants decompositions of random surfaces, Geom. Funct. Anal., Volume 21 (2011) no. 5, pp. 1069-1090 | DOI | MR | Zbl

[Hat07] Hatcher, Allen Notes on Basic $3$-Manifold Topology (2007) (Lecture notes, available at: http://pi.math.cornell.edu/~hatcher/3M/3Mdownloads.html)

[Hay56] Hayman, Walter K. A generalisation of Stirling’s formula, J. Reine Angew. Math., Volume 196 (1956), pp. 67-95 | DOI | MR | Zbl

[Hem87] Hempel, John Residual finiteness for $3$-manifolds, Combinatorial group theory and topology (Alta, Utah, 1984) (Annals of Mathematics Studies), Volume 111, Princeton University Press, 1987, pp. 379-396 | DOI | MR | Zbl

[HS68] Harris, Bernard; Schoenfeld, Lowell Asymptotic expansions for the coefficients of analytic functions, Ill. J. Math., Volume 12 (1968), pp. 264-277 | MR | Zbl

[HV22] Hamenstädt, Ursula; Viaggi, Gabriele Small eigenvalues of random 3-manifolds, Trans. Am. Math. Soc., Volume 375 (2022) no. 6, pp. 3795-3840 | DOI | MR | Zbl

[Kam19] Kammeyer, Holger Introduction to ${\ell }^2$-invariants, Lecture Notes in Mathematics, 2247, Springer, 2019 | DOI | MR | Zbl

[Kel20] Kelley, Andrew James Subgroup growth of all Baumslag–Solitar groups, New York J. Math., Volume 26 (2020), pp. 218-229 | MR | Zbl

[LM00] Liskovets, Valery; Mednykh, Alexander Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. Algebra, Volume 28 (2000) no. 4, pp. 1717-1738 | DOI | MR | Zbl

[LS03] Lubotzky, Alexander; Segal, Dan Subgroup growth, Progress in Mathematics, 212, Birkhäuser, 2003 | DOI | MR | Zbl

[LS04] Liebeck, Martin W.; Shalev, Aner Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks, J. Algebra, Volume 276 (2004) no. 2, pp. 552-601 | DOI | MR | Zbl

[Lüc94] Lück, Wolfgang Approximating $L^2$-invariants by their finite-dimensional analogues, Geom. Funct. Anal., Volume 4 (1994) no. 4, pp. 455-481 | DOI | MR | Zbl

[Lüc02] Lück, Wolfgang $L^2$-invariants: theory and applications to geometry and $K$-theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 44, Springer, 2002 | DOI | MR | Zbl

[Mah10] Maher, Joseph Random Heegaard splittings, J. Topol., Volume 3 (2010) no. 4, pp. 997-1025 | DOI | MR | Zbl

[Mir13] Mirzakhani, Maryam Growth of Weil–Petersson volumes and random hyperbolic surfaces of large genus, J. Differ. Geom., Volume 94 (2013) no. 2, pp. 267-300 | MR | Zbl

[MNP22] Magee, Michael; Naud, Frédéric; Puder, Doron A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16}-\epsilon$, Geom. Funct. Anal., Volume 32 (2022) no. 3, pp. 595-661 | DOI | MR | Zbl

[MP19] Mirzakhani, Maryam; Petri, Bram Lengths of closed geodesics on random surfaces of large genus, Comment. Math. Helv., Volume 94 (2019) no. 4, pp. 869-889 | DOI | MR | Zbl

[MP23] Magee, Michael; Puder, Doron The Asymptotic Statistics of Random Covering Surfaces, Forum Math. Pi, Volume 11 (2023), e15 | DOI | MR | Zbl

[MRR22] Masur, Howard; Rafi, Kasra; Randecker, Anja Expected covering radius of a translation surface, Int. Math. Res. Not., Volume 2022 (2022) no. 10, pp. 7967-8002 | DOI | MR | Zbl

[MSP02] Müller, Thomas W.; Schlage-Puchta, Jan-Christoph Character theory of symmetric groups and subgroup growth of surface groups, J. Lond. Math. Soc., Volume 66 (2002) no. 3, pp. 623-640 | DOI | MR | Zbl

[MSP04] Müller, Thomas W.; Schlage-Puchta, Jan-Christoph Classification and statistics of finite index subgroups in free products, Adv. Math., Volume 188 (2004) no. 1, pp. 1-50 | DOI | MR | Zbl

[MSP10] Müller, Thomas W.; Schlage-Puchta, Jan-Christoph Statistics of isomorphism types in free products, Adv. Math., Volume 224 (2010) no. 2, pp. 707-730 | DOI | MR | Zbl

[MW55] Moser, Leo; Wyman, Max On solutions of $x^d=1$ in symmetric groups, Can. J. Math., Volume 7 (1955), pp. 159-168 | DOI | MR | Zbl

[Mül96] Müller, Thomas W. Subgroup growth of free products, Invent. Math., Volume 126 (1996) no. 1, pp. 111-131 | DOI | MR | Zbl

[Mül97] Müller, Thomas W. Finite group actions and asymptotic expansion of $e^{P\left(z\right)}$, Combinatorica, Volume 17 (1997) no. 4, pp. 523-554 | DOI | MR | Zbl

[Nic94] Nica, Alexandru On the number of cycles of given length of a free word in several random permutations, Random Struct. Algorithms, Volume 5 (1994) no. 5, pp. 703-730 | DOI | MR | Zbl

[Pav82] Pavlov, Aleksander I. On the limit distribution of the number of solutions of the equation $x^k=a$ in the symmetric group $S_n$, Mat. Sb., N. Ser., Volume 117(159) (1982) no. 2, pp. 239-250 | MR | Zbl

[Pet17] Petri, Bram Random regular graphs and the systole of a random surface, J. Topol., Volume 10 (2017) no. 1, pp. 211-267 | DOI | MR | Zbl

[PT18] Petri, Bram; Thäle, Christoph Poisson approximation of the length spectrum of random surfaces, Indiana Univ. Math. J., Volume 67 (2018) no. 3, pp. 1115-1141 | DOI | MR | Zbl

[Pud15] Puder, Doron Expansion of random graphs: new proofs, new results, Invent. Math., Volume 201 (2015) no. 3, pp. 845-908 | DOI | MR | Zbl

[PZ22] Puder, Doron; Zimhoni, Tomer Local Statistics of Random Permutations from Free Products (2022) (https://arxiv.org/abs/2203.12250)

[SDS99] du Sautoy, Marcus P. F.; McDermott, John J.; Smith, Geoff C. Zeta functions of crystallographic groups and analytic continuation, Proc. Lond. Math. Soc., Volume 79 (1999) no. 3, pp. 511-534 | DOI | MR | Zbl

[Shr22] Shrestha, Sunrose The topology and geometry of random square-tiled surfaces, Geom. Dedicata, Volume 216 (2022) no. 4, 38 | DOI | MR | Zbl

[Sul16] Sulca, Diego Zeta functions of virtually nilpotent groups, Isr. J. Math., Volume 213 (2016) no. 1, pp. 371-398 | DOI | MR | Zbl

[Ver12] Vershik, Anatoliĭ M. Totally nonfree actions and the infinite symmetric group, Mosc. Math. J., Volume 12 (2012) no. 1, p. 193-212, 216 | DOI | MR | Zbl

[Vol86] Volynets, L. M. The number of solutions of the equation $x^s=e$ in a symmetric group, Mat. Zametki, Volume 40 (1986) no. 2, pp. 155-160 | MR | Zbl

[Wil86] Wilf, Herbert S. The asymptotics of $e^{P\left(z\right)}$ and the number of elements of each order in $S_n$, Bull. Am. Math. Soc., Volume 15 (1986) no. 2, pp. 228-232 | DOI | MR | Zbl

[Wor99] Wormald, Nicholas C. Models of random regular graphs, Surveys in combinatorics, 1999 (Canterbury) (London Mathematical Society Lecture Note Series), Volume 267, Cambridge University Press, 1999, pp. 239-298 | DOI | MR | Zbl