Charles Bordenave

This is an old revision of the document!

Most of my publications and preprint are available on arxiv. For a recent publication list, see here.

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<LI> Mobility Edge of Lévy Matrices with A. Aggarwal and P. Lopatto Preprint <A HREF=“https://arxiv.org/abs/2210.09458” target=“_blank”> arXiv:2210.09458</A>.

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<LI> Noise sensitivity for the top eigenvector of a sparse random matrix with J. Lee Electron. J. Probab. 27 (2022), Paper No. 49 <A HREF=“https://arxiv.org/abs/2106.09570” target=“_blank”> arXiv:2106.09570</A>.

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<LI> Existence of absolutely continuous spectrum for Galton-Watson random trees with A. Arras Preprint <A HREF=“https://arxiv.org/abs/2105.10177” target=“_blank”> arXiv:2105.10177</A>.

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<LI> 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. <A HREF=“https://arxiv.org/abs/2102.02653” target=“_blank”> arXiv:2102.02653</A>.

</LI> <LI> Strong asymptotic freeness for independent uniform variables on compact groups associated to non-trivial representations with B. Collins Preprint <A HREF=“https://arxiv.org/abs/2012.08759” target=“_blank”> arXiv:2012.08759</A>.

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<LI> 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. <A HREF=“https://arxiv.org/abs/2012.05602” target=“_blank”> arXiv:2012.05602</A>.

</LI> <LI> Markovian linearization of random walks on groups with B. Dubail To appear in International Mathematics Research Notices. <A HREF=“https://arxiv.org/abs/2011.14127” target=“_blank”> arXiv:2011.14127</A>.

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Detection thresholds in very sparse matrix completion with S. Coste and R. R. Nadakuditi To appear in Foundations of Computational Mathematics. <A HREF=“https://arxiv.org/abs/2005.06062” target=“_blank”> arXiv:2005.06062</A>.

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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. <A HREF=“http://arxiv.org/abs/1906.10674” target=“_blank”> arXiv:1906.10674</A>.

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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. <A HREF=“http://arxiv.org/abs/1903.04869” target=“_blank”> arxiv:1903.04869</A>.

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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. <A HREF=“http://arxiv.org/abs/1812.06769” target=“_blank”> arxiv:1812.06769</A>.

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Spectral gap of sparse bistochastic matrices with exchangeable rows with

application to shuffle-and-fold maps   <br >

with Y. Qiu and Y. Zhang Annales de l’Institut Henri Poincar&eacute (B) 56(4):2971–2995, 2020. <A HREF=“http://arxiv.org/abs/1805.06205” target=“_blank”> arxiv:1805.06205</A>.

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Eigenvalues of random lifts and polynomial of random permutation matrices with B. Collins Ann. of Math. (2), 190(3) : 811–875, 2019. <A HREF=“http://arxiv.org/abs/1801.00876” target=“_blank”> arxiv:1801.00876</A>.

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Graphs with prescribed local neighborhoods of their universal coverings with S. Coste J. Combin. Theory Ser. B, 138:196–205, 2019. <A HREF=“http://arxiv.org/abs/1712.03520” target=“_blank”> arxiv:1712.03520</A>.

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Largest eigenvalues of sparse inhomogeneous Erd&oumls-R&eacutenyi graphs with F. Benaych-Georges and A. Knowles Annals of Probability, 47(3):1653–1676, 2019. <A HREF=“http://arxiv.org/abs/1704.02953” target=“_blank”> arxiv:1704.02953</A>.

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Spectral radii of sparse random matrices with F. Benaych-Georges and A. Knowles Ann. Inst. Henri Poincaré (B) 56(3), 2141–2161, 2020. <A HREF=“https://arxiv.org/abs/1704.02945” target=“_blank”> arxiv:1704.02945</A>.

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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. <A HREF=“http://arxiv.org/abs/1611.01079” target=“_blank”> arxiv:1611.01079</A>.

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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. <A HREF=“http://arxiv.org/abs/1610.01836” target=“_blank”> arxiv:1610.01836</A>.

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On the spectral radius of a random matrix with P. Caputo, D. Chafai and K. Tikhomirov Annals of Probability, 46(4):2268–2286, 2018. <A HREF=“http://arxiv.org/abs/1607.05484” target=“_blank”> arxiv:1607.05484</A>.

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Shotgun Assembly of Random Jigsaw Puzzles with U. Feige and E. Mossel Random Structures Algorithms 56(4), 998–1015, 2020. <A HREF=“http://arxiv.org/abs/1605.03086” target=“_blank”> arxiv:1605.03086</A>.

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Delocalization at small energy for heavy-tailed random matrices with A. Guionnet Communications in Mathematical Physics, 354(1):115–159, 2017. <A HREF=“http://arxiv.org/abs/1603.08845” target=“_blank”> arxiv:1603.08845</A>.

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Random walk on sparse random digraphs with P. Caputo and J. Salez Probability Theory and Related Fields, 170(3-4):933–960, 2018. <A HREF=“http://arxiv.org/abs/1508.06600” target=“_blank”> arxiv:1508.06600</A>.

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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. <A HREF=“http://arxiv.org/abs/1502.04482” target=“_blank”> arxiv:1502.04482</A>. </LI>

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Non-backtracking spectrum of random graphs: community detection and non-regular Ramanujan graphs with M. Lelarge and L. Massouli&eacute Annals of Probability, 46(1):1–71, 2018 and FOCS 2015 <A HREF=“http://arxiv.org/abs/1501.06087” target=“_blank”> arxiv:1501.06087</A>. </LI>

<LI> On quantum percolation in finite regular graphs Annales Henri Poincar&eacute 16 (2015), no. 11, 2465-2497 <A HREF=“http://arxiv.org/abs/1409.2000” target=“_blank”> arxiv:1409.2000</A>. </LI>

<LI> Outlier eigenvalues for deformed i.i.d. random matrices with M. Capitaine Communications in Pure and Applied Mathematics, Vol. 69 (11), 2131-2194 (2016) <A HREF=“http://arxiv.org/abs/1403.6001” target=“_blank”> arxiv:1403.6001</A>. </LI>

<LI> An extension of the Derrida-Lebowitz-Speer-Spohn equation with P. Germain and T. Trogdon Journal of Physics A, no. 48, 485205 (2015). <A HREF=“http://arxiv.org/abs/1402.6620” target=“_blank”> arxiv:1402.6620</A>. </LI>

<LI> 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) <A HREF=“http://arxiv.org/abs/1308.5725” target=“_blank”> arxiv:1308.5725</A>. </LI>

<LI> Mean quantum percolation with A. Sen and B. Virag Journal of the European Mathematical Society, 19(12):3679–3707, 2017. <A HREF=“http://arxiv.org/abs/1308.3755” target=“_blank”> arxiv:1308.3755</A>. </LI>

<LI> Extinction probability and total progeny of predator-prey dynamics on

infinite trees  <br >

Electronic Journal in Probability, Vol. 19(20), 1-33 (2014) <A HREF=“http://arxiv.org/abs/1210.2883” target=“_blank”> arxiv:1210.2883</A>. </LI>

<LI> On Euclidean random matrices in high dimension Electronic Communications in Probability, Vol. 18, 1-8 (2013) <A HREF=“http://arxiv.org/abs/1209.5888” target=“_blank”> arxiv:1209.5888</A>. </LI>

<LI> A large deviations principle for Wigner matrices without gaussian tails with P. Caputo Annals of Probability 42 (2014), no. 6, 2454-2496. <A HREF=“http://arxiv.org/abs/1207.5570” target=“_blank”> arxiv:1207.5570</A>. </LI>

<LI> 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) <A HREF=“http://arxiv.org/abs/1202.0644” target=“_blank”> arxiv:1202.0644</A>. </LI>

<LI> 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) <A HREF=“http://arxiv.org/abs/1201.1862” target=“_blank”> arxiv:1201.1862</A>. </LI>

<LI> Around the circular law with D. Chafai Probability Surveys, Vol. 9(0), 1-89 (2012) <A HREF=“http://arxiv.org/abs/1109.3343” target=“_blank”> arxiv:1109.3343</A>. </LI>

<LI> Combinatorial optimization over two random point sets with F. Barthe S&eacuteminaire de probabilit&eacutes XLV Vol. 2046, 483-536 (2013) <A HREF=“http://arxiv.org/abs/1103.2734” target=“_blank”> arxiv:1103.2734</A>. </LI>

<LI> Matchings on infinite graphs with M. Lelarge and J. Salez Probability Theory and Related Fields, Vol. 157(1), 183-208 (2013) <A HREF=“http://arxiv.org/abs/1102.0712” target=“_blank”> arxiv:1102.0712</A>. </LI>

<LI> On the spectrum of sum and product of non-hermitian random matrices Electronic Communications in Probability, Vol. 16, 104-113 (2011) <A HREF=“http://arxiv.org/abs/1010.3087” target=“_blank”> arxiv:1010.3087</A>. </LI>

<LI> Spectrum of non-Hermitian heavy tailed random matrices with P. Caputo and D. Chafai Communications in Mathematical Physics, Vol. 307(2), 513-560 (2011) <A HREF=“http://arxiv.org/abs/1006.1713” target=“_blank”> arxiv:1006.1713</A>. </LI>

<LI> 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) <A HREF=“http://arxiv.org/abs/0808.1502” target=“_blank”> arxiv:0808.1502</A>. </LI>

<LI> The rank of diluted random graphs with M. Lelarge and J. Salez Annals of Probability, Vol. 39(3), 1097-1121 (2011) <A HREF=“http://arxiv.org/abs/0907.4244” target=“_blank”> arxiv:0907.4244</A>. </LI>

<LI> 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). <A HREF=“http://arxiv.org/abs/0903.3528” target=“_blank”> arxiv:0903.3528</A>. </LI>

<LI> Load optimization in a planar network with G.L. Torrisi Annals of Applied Probability, Vol. 20(6), 2040-2085 (2010) <A HREF=“http://fr.arxiv.org/abs/0902.4304” target=“_blank”>arxiv:0902.4304</A>. </LI>

<LI> Spectrum of large random reversible Markov chains : two

            examples  <br >

with P. Caputo and D. Chafai Latin American Journal of Probability and Mathematical Statistics, Vol. 7, 41-64 (2010) <A HREF=“http://arxiv.org/abs/0811.1097” target=“_blank”>arxiv:0811.1097</A>. </LI>

<LI> Asymptotic stability region of slotted-Aloha with D. McDonald and A. Proutière IEEE Transactions on Information Theory, Vol. 58(9), 5841-5855 (2012) <A HREF=“http://arxiv.org/abs/0809.5023” target=“_blank”>arxiv:0809.5023</A>. </LI>

<LI> Performance of random medium access control, an asymptotic approach with D. McDonald and A. Proutière Proc. ACM Sigmetrics 2008, 1-12, (2008) <A HREF=“https://hal.inria.fr/hal-00849006v1” target=“_blank”>hal-inria-00849006</A>. </LI>

<LI> On the birth-and-assassination process, with an application to scotching a rumor in a network Electronic Journal of Probability, 2014-2030, (2008) <A HREF=“ http://arxiv.org/abs/0801.4499” target=“_blank”>arxiv:0801.4499</A>. </LI>

<LI> Resolvent of Large Random Graphs with M. Lelarge Random Structures & Algorithms, Vol. 37(3), 332-352, (2010) <A HREF=“http://arxiv.org/abs/0801.0155” target=“_blank”>arxiv:0801.0155</A>. </LI>

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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) <A HREF=“http://arxiv.org/abs/0710.0857” target=“_blank”> arxiv: math.PR/0710.0857</A>. </LI>

<LI> A particle system in interaction with a rapidly varying environment: Mean field limits and applications with D. McDonald and A. Proutière Networks and Heterogeneous Media, Vol 5, No.1 (2010) <A HREF=“http://arxiv.org/abs/math/0701363” target=“_blank”>arxiv: math.PR/0701363</A>.

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<LI> Near-Minimal Spanning Trees: a Scaling Exponent in Probability Models with D. Aldous and M. Lelarge Annales de l'Institut Henri Poincar&eacute (B) Vol. 44, No. 5 (2008) <A HREF=“http://arxiv.org/abs/math.PR/0609547” target=“_blank”>arxiv: math.PR/0609547</A>. </LI>

<LI> Navigation on a Poisson point process Annals of Applied Probability , Vol. 18, No. 2, 708-746 (2008) <A HREF=“http://arxiv.org/abs/math.PR/0601122” target=“_blank”>arxiv: math.PR/0601122 </A>. </LI>

<LI> The radial spanning tree of a Poisson point process with F. Baccelli Annals of Applied Probability, Vol. 17, No. 1, 305-359 (2007) <A HREF=“http://arxiv.org/abs/math/0703024”>arxiv: math/0703024</A>. </LI>

<LI> Eigenvalues of Euclidean random matrices </A> Random Structures & Algorithms, Vol. 33, No. 4, 515-532 (2008) <A HREF=“http://arxiv.org/abs/math.PR/0606624” target=“_blank”>arxiv: math.PR/0606624</A>. </LI>

<LI> A random multiple access protocol with spatial interactions with S. Foss and V. Shneer Journal of Applied Probability, Vol. 46, 844-865 (2009) <A HREF=“http://arxiv.org/abs/math.PR/0612583” target=“_blank”>arxiv: math.PR/0612583</A>. </LI>

<LI> Large deviations of Poisson cluster processes with G.L. Torrisi Stochastic Models, Vol 23, 593-625 (2007) . </LI>

<LI> Monte Carlo methods for sensitivity analysis of Poisson-driven stochastic systems </A> with G.L. Torrisi Advances in Applied Probability, vol. 40(2):293-320 (2008). </LI>

<LI> Random multi-access algorithms, a mean field analysis</A> with D. Mc Donald and A. Proutière Proc. 43th Allerton conference (2005) <A HREF=“https://hal.inria.fr/inria-00070375/” target=“_blank”>hal-inria-00070375</A>. </LI>

<LI> Stability of spatial networks</A> Advances in Applied Probability, vol. 38-8 (2006). </LI>

<Li> Spatial capacity of multiple access wireless networks IEEE Transactions on Information Theory, vol. 52-11 (2006). </LI>

<LI> The dead leaves model: a general tessellation modelling occlusion with Y. Gousseau and F. Roueff Advances in Applied Probability, vol. 38-1 (2006). </LI>

Some papers and preprints