Most of my publications and preprint are available on [[https://arxiv.org/search/advanced?advanced=1&terms-0-operator=AND&terms-0-term=Bordenave%2C+Charles&terms-0-field=author&classification-mathematics=y&classification-physics_archives=all&classification-include_cross_list=include&date-filter_by=all_dates&date-year=&date-from_date=&date-to_date=&date-date_type=submitted_date&abstracts=show&size=50&order=-announced_date_first|arxiv]]. For a recent publication list, see {{ :publication_list.pdf|here}}. ---- {{::nuage-de-mots.png?800|}} ---- ==== Some papers and preprints ==== Norm of matrix-valued polynomials in random unitaries and permutations, with B. Collins, //Preprint// [[ https://arxiv.org/abs/2304.05714|arXiv:2304.05714]]. \\ Mobility Edge of Lévy Matrices, with A. Aggarwal and P. Lopatto, //Preprint// [[ https://arxiv.org/abs/2210.09458 | arXiv:2210.09458]]. \\ Noise sensitivity for the top eigenvector of a sparse random matrix, with J. Lee, // Electron. J. Probab. 27 (2022), Paper No. 49 // [[ https://arxiv.org/abs/2106.09570 | arXiv:2106.09570]]. \\ Existence of absolutely continuous spectrum for Galton-Watson random trees, with A. Arras, // to appear Communications in Mathematical Physics // [[ https://arxiv.org/abs/2105.10177" target="_blank | arXiv:2105.10177]]. \\ Typicality and entropy of processes on infinite trees, A. Backhausz and B. Szegedy, // Ann. Inst. Henri Poincaré Probab. Stat. 58 (2022), no. 4, 1959–1980 // [[ https://arxiv.org/abs/2102.02653" target="_blank" | arXiv:2102.02653]]. \\ Strong asymptotic freeness for independent uniform variables on compact groups associated to non-trivial representations, with B. Collins, // To appear in Invent. Math.// [[ https://arxiv.org/abs/2012.08759" target="_blank" | arXiv:2012.08759]]. \\ Convergence of the spectral radius of a random matrix through its characteristic polynomial with D. Chafai and D. Garcia-Zelada // Probab. Theory Related Fields 182 (2022), no. 3-4, 1163–1181. // [[ https://arxiv.org/abs/2012.05602" target="_blank" | arXiv:2012.05602]]. \\ Markovian linearization of random walks on groups with B. Dubail, // To appear in International Mathematics Research Notices // [[ https://arxiv.org/abs/2011.14127" target="_blank" | arXiv:2011.14127 ]]. \\ Detection thresholds in very sparse matrix completion with S. Coste and R. R. Nadakuditi // To appear in Foundations of Computational Mathematics. // [[ https://arxiv.org/abs/2005.06062" target="_blank" | arXiv:2005.06062 ]]. \\ Outlier eigenvalues for non-Hermitian polynomials in independent i.i.d. matrices and deterministic matrices with S. Belinschi, M. Capitaine and G. Cébron // Electron. J. Probab. 26 (2021): Paper No. 100, 37 pp. // [[http://arxiv.org/abs/1906.10674" target="_blank" | arXiv:1906.10674]]. \\ Noise sensitivity of the top eigenvector of a Wigner matrix with G. Lugosi and N. Zhivotovskiy // Probab. Theory Related Fields, 177(3-4):1103–1135, 2020. // [[http://arxiv.org/abs/1903.04869" target="_blank" | arxiv:1903.04869]]. \\ Cutoff at the entropic time for random walks on covered expander graphs with H. Lacoin // J. Inst. Math. Jussieu 21 (2022), no. 5, 1571–1616. // [[http://arxiv.org/abs/1812.06769" target="_blank" | arxiv:1812.06769]]. \\ Spectral gap of sparse bistochastic matrices with exchangeable rows with application to shuffle-and-fold maps with Y. Qiu and Y. Zhang // Annales de l’Institut Henri Poincaré (B) 56(4):2971–2995, 2020. // [[http://arxiv.org/abs/1805.06205" target="_blank" | arxiv:1805.06205]]. \\ Eigenvalues of random lifts and polynomial of random permutation matrices with B. Collins // Ann. of Math. (2), 190(3) : 811–875, 2019. // [[http://arxiv.org/abs/1801.00876" target="_blank" | arxiv:1801.00876]]. \\ Graphs with prescribed local neighborhoods of their universal coverings with S. Coste // J. Combin. Theory Ser. B, 138:196–205, 2019. // [[http://arxiv.org/abs/1712.03520" target="_blank" | arxiv:1712.03520]]. \\ Largest eigenvalues of sparse inhomogeneous Erdös-Rényi graphs with F. Benaych-Georges and A. Knowles // Annals of Probability, 47(3):1653–1676, 2019. // [[http://arxiv.org/abs/1704.02953" target="_blank" | arxiv:1704.02953]]. \\ Spectral radii of sparse random matrices with F. Benaych-Georges and A. Knowles // Ann. Inst. Henri Poincaré (B) 56(3), 2141–2161, 2020.// [[https://arxiv.org/abs/1704.02945" target="_blank" | arxiv:1704.02945]]. \\ Cutoff at the "entropic time" for sparse Markov chains with P. Caputo and J. Salez // Probability Theory and Related Fields, 173(1-2):261–292, 2019. // [[http://arxiv.org/abs/1611.01079" target="_blank" | arxiv:1611.01079]]. \\ Spectrum of large random Markov chains: heavy-tailed weights on the oriented complete graph with P. Caputo, D. Chafai and D. Piras // Random Matrices: Theory and Applications, 6 (2017), no. 2, 1750006, 33 pp. // [[http://arxiv.org/abs/1610.01836" target="_blank" | arxiv:1610.01836]]. \\ On the spectral radius of a random matrix with P. Caputo, D. Chafai and K. Tikhomirov // Annals of Probability, 46(4):2268–2286, 2018. // [[http://arxiv.org/abs/1607.05484" target="_blank" | arxiv:1607.05484]]. \\ Shotgun Assembly of Random Jigsaw Puzzles with U. Feige and E. Mossel // Random Structures Algorithms 56(4), 998–1015, 2020. // [[http://arxiv.org/abs/1605.03086" target="_blank" | arxiv:1605.03086]]. \\ Delocalization at small energy for heavy-tailed random matrices with A. Guionnet // Communications in Mathematical Physics, 354(1):115–159, 2017. // [[http://arxiv.org/abs/1603.08845" target="_blank" | arxiv:1603.08845]]. \\ Random walk on sparse random digraphs with P. Caputo and J. Salez // Probability Theory and Related Fields, 170(3-4):933–960, 2018. // [[http://arxiv.org/abs/1508.06600" target="_blank" | arxiv:1508.06600]]. \\ A new proof of Friedman's second eigenvalue Theorem and its extension to random lifts // Ann. Sci. Éc. Norm. Supér. (4) 53 (2020), no. 6, 1393–1439. // [[http://arxiv.org/abs/1502.04482" target="_blank" | arxiv:1502.04482]]. \\ Non-backtracking spectrum of random graphs: community detection and non-regular Ramanujan graphs with M. Lelarge and L. Massoulié // Annals of Probability, 46(1):1–71, 2018 and FOCS 2015 // [[http://arxiv.org/abs/1501.06087" target="_blank" | arxiv:1501.06087]]. \\ On quantum percolation in finite regular graphs // Annales Henri Poincaré 16 (2015), no. 11, 2465-2497// [[http://arxiv.org/abs/1409.2000" target="_blank" | arxiv:1409.2000]]. \\ Outlier eigenvalues for deformed i.i.d. random matrices with M. Capitaine // Communications in Pure and Applied Mathematics, Vol. 69 (11), 2131-2194 (2016) // [[http://arxiv.org/abs/1403.6001" target="_blank" | arxiv:1403.6001]]. \\ An extension of the Derrida-Lebowitz-Speer-Spohn equation with P. Germain and T. Trogdon // Journal of Physics A, no. 48, 485205 (2015).// [[http://arxiv.org/abs/1402.6620" target="_blank" | arxiv:1402.6620]]. \\ Large deviations of empirical neighborhood distribution in sparse random graphs with P. Caputo // Probability Theory and Related Fields, 163 no. 1-2, 149-222 (2015) // [[http://arxiv.org/abs/1308.5725" target="_blank" | arxiv:1308.5725]]. \\ Mean quantum percolation with A. Sen and B. Virag // Journal of the European Mathematical Society, 19(12):3679–3707, 2017. // [[http://arxiv.org/abs/1308.3755" target="_blank" | arxiv:1308.3755]]. \\ Extinction probability and total progeny of predator-prey dynamics on infinite trees // Electronic Journal in Probability, Vol. 19(20), 1-33 (2014) // [[http://arxiv.org/abs/1210.2883" target="_blank" | arxiv:1210.2883]]. \\ On Euclidean random matrices in high dimension // Electronic Communications in Probability, Vol. 18, 1-8 (2013) // [[http://arxiv.org/abs/1209.5888" target="_blank" | arxiv:1209.5888]]. \\ A large deviations principle for Wigner matrices without gaussian tails with P. Caputo // Annals of Probability 42 (2014), no. 6, 2454-2496. // [[http://arxiv.org/abs/1207.5570" target="_blank" | arxiv:1207.5570]]. \\ Spectrum of Markov generators on sparse random graphs with P. Caputo and D. Chafai // Communications in Pure and Applied Mathematics, Vol.67(4) 621-669 (2014) // [[http://arxiv.org/abs/1202.0644" target="_blank" | arxiv:1202.0644]]. \\ Localization and delocalization of eigenvectors for heavy-tailed random matrices with A. Guionnet // Probability Theory and Related Fields, Vol. 157(3-4), 885-953 (2013) // [[http://arxiv.org/abs/1201.1862" target="_blank" | arxiv:1201.1862]]. \\ Around the circular law with D. Chafai // Probability Surveys, Vol. 9(0), 1-89 (2012) // [[http://arxiv.org/abs/1109.3343" target="_blank" | arxiv:1109.3343]]. \\ Combinatorial optimization over two random point sets with F. Barthe // Séminaire de probabilités XLV Vol. 2046, 483-536 (2013) // [[http://arxiv.org/abs/1103.2734" target="_blank" | arxiv:1103.2734]]. \\ Matchings on infinite graphs with M. Lelarge and J. Salez // Probability Theory and Related Fields, Vol. 157(1), 183-208 (2013) // [[http://arxiv.org/abs/1102.0712" target="_blank" | arxiv:1102.0712]]. \\ On the spectrum of sum and product of non-hermitian random matrices // Electronic Communications in Probability, Vol. 16, 104-113 (2011) // [[http://arxiv.org/abs/1010.3087" target="_blank" | arxiv:1010.3087]]. \\ Spectrum of non-Hermitian heavy tailed random matrices with P. Caputo and D. Chafai // Communications in Mathematical Physics, Vol. 307(2), 513-560 (2011) // [[http://arxiv.org/abs/1006.1713" target="_blank" | arxiv:1006.1713]]. \\ Circular Law Theorem for Random Markov Matrices with P. Caputo and D. Chafai // Probability Theory and Related Fields, Vol. 152(3-4), 751-779 (2012) // [[http://arxiv.org/abs/0808.1502" target="_blank" | arxiv:0808.1502]]. \\ The rank of diluted random graphs with M. Lelarge and J. Salez // Annals of Probability, Vol. 39(3), 1097-1121 (2011) // [[http://arxiv.org/abs/0907.4244" target="_blank" | arxiv:0907.4244]]. \\ Spectrum of large random reversible Markov chains - heavy-tailed weights on the complete graph with P. Caputo and D. Chafai // Annals of Probability, Vol. 39(4), 1544-1590 (2011). // [[http://arxiv.org/abs/0903.3528" target="_blank" | arxiv:0903.3528]]. \\ Load optimization in a planar network with G.L. Torrisi // Annals of Applied Probability, Vol. 20(6), 2040-2085 (2010) // [[http://fr.arxiv.org/abs/0902.4304" target="_blank" |arxiv:0902.4304]]. \\ Spectrum of large random reversible Markov chains : two examples with P. Caputo and D. Chafai // Latin American Journal of Probability and Mathematical Statistics, Vol. 7, 41-64 (2010) // [[http://arxiv.org/abs/0811.1097" target="_blank" |arxiv:0811.1097]]. \\ Asymptotic stability region of slotted-Aloha with D. McDonald and A. Proutiè;re // IEEE Transactions on Information Theory, Vol. 58(9), 5841-5855 (2012) // [[http://arxiv.org/abs/0809.5023" target="_blank" |arxiv:0809.5023]]. \\ Performance of random medium access control, an asymptotic approach with D. McDonald and A. Proutiè;re // Proc. ACM Sigmetrics 2008, 1-12, (2008)// [[https://hal.inria.fr/hal-00849006v1" target="_blank" | hal-inria-00849006]]. \\ On the birth-and-assassination process, with an application to scotching a rumor in a network // Electronic Journal of Probability, 2014-2030, (2008) // [[ http://arxiv.org/abs/0801.4499" target="_blank" |arxiv:0801.4499]]. \\ Resolvent of Large Random Graphs with M. Lelarge // Random Structures & Algorithms, Vol. 37(3), 332-352, (2010) // [[http://arxiv.org/abs/0801.0155" target="_blank" |arxiv:0801.0155]]. \\ Dynamic Programming Optimization over Random Data: the Scaling Exponent for Near-optimal Solutions with D. Aldous and M. Lelarge // SIAM Journal of Computing, Vol.38, No.6 (2009) // [[http://arxiv.org/abs/0710.0857" target="_blank" | arxiv: math.PR/0710.0857]]. \\ A particle system in interaction with a rapidly varying environment: Mean field limits and applications with D. McDonald and A. Proutiè;re // Networks and Heterogeneous Media, Vol 5, No.1 (2010) // [[http://arxiv.org/abs/math/0701363" target="_blank" |arxiv: math.PR/0701363]]. \\ Near-Minimal Spanning Trees: a Scaling Exponent in Probability Models with D. Aldous and M. Lelarge // Annales de l'Institut Henri Poincaré (B) Vol. 44, No. 5 (2008) // [[http://arxiv.org/abs/math.PR/0609547" target="_blank" |arxiv: math.PR/0609547]]. \\ Navigation on a Poisson point process // Annals of Applied Probability , Vol. 18, No. 2, 708-746 (2008) // [[http://arxiv.org/abs/math.PR/0601122" target="_blank" |arxiv: math.PR/0601122 ]]. \\ The radial spanning tree of a Poisson point process with F. Baccelli // Annals of Applied Probability, Vol. 17, No. 1, 305-359 (2007) //[[http://arxiv.org/abs/math/0703024" |arxiv: math/0703024]]. \\ Eigenvalues of Euclidean random matrices ]] // Random Structures & Algorithms, Vol. 33, No. 4, 515-532 (2008) // [[http://arxiv.org/abs/math.PR/0606624" target="_blank" |arxiv: math.PR/0606624]]. \\ A random multiple access protocol with spatial interactions with S. Foss and V. Shneer // Journal of Applied Probability, Vol. 46, 844-865 (2009) // [[http://arxiv.org/abs/math.PR/0612583" target="_blank" |arxiv: math.PR/0612583]]. \\ Large deviations of Poisson cluster processes with G.L. Torrisi // Stochastic Models, Vol 23, 593-625 (2007) //. \\ Monte Carlo methods for sensitivity analysis of Poisson-driven stochastic systems ]] with G.L. Torrisi // Advances in Applied Probability, vol. 40(2):293-320 (2008). // \\ Random multi-access algorithms, a mean field analysis]] with D. Mc Donald and A. Proutiè;re //Proc. 43th Allerton conference (2005)//[[https://hal.inria.fr/inria-00070375/" target="_blank" | hal-inria-00070375]]. \\ Stability of spatial networks]] // Advances in Applied Probability, vol. 38-8 (2006)//. \\ Spatial capacity of multiple access wireless networks // IEEE Transactions on Information Theory, vol. 52-11 (2006)//. \\ The dead leaves model: a general tessellation modelling occlusion with Y. Gousseau and F. Roueff // Advances in Applied Probability, vol. 38-1 (2006).//