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I am a lecturer at the University of Bath, where I am a member of the probability group Prob-L@B. Between 2018 and 2021, I was an EPSRC postdoctoral fellow (title of the fellowship: "Random trees: analysis and applications"). Between 2013 and 2016, I was a postdoc at Prob-L@B, as part of Peter Mörters' EPSRC project Emergence of Condensation in Stochastic Networks. Between 2010 and 2013, I was a PhD student whithin the Laboratoire de Mathématiques de Versailles under the supervision of Brigitte Chauvin and Danièle Gardy.

I am interested in:

• branching processes, random trees
• reinforcement, Pólya urns and stochastic approximation
• random networks, preferential attachment
• statistical physics: zero-range model, preferential attachment
• satisfiability, random Boolean trees and analytic combinatorics

I have been serving as an Associate Editor of the Applied Probability Trust (since October 2020), and of Stochastic Processes and Their Applications (since March 2022).

I wrote a general introduction to Pólya urns for the LMS Newsletter (November 2020, page 24). The intended audience is mathematicians in all areas of maths, starting at postgraduate level: the non-official title is "Why do probabilists still study coloured balls being drawn from urns?" [pdf]

News

Maternity leave

I will be on maternity leave until January 2023. I am still checking emails regularly, but might be slow to reply.

British Mathematical Colloquium 2023

I am part of the organising committee of the next BMC (chair: Kirill Cherednichenko), to be held at the University of Bath, April 3-6, 2023. There is more information on the website.

Publications

Preprints

• Scaling limit of critical random trees in random environment (52 pages)
  Guillaume Conchon-Kerjan, Daniel Kious, and Cécile Mailler.
  
• Fluctuations of balanced urns with infinitely many colours (60 pages)
  Svante Janson, Cécile Mailler and Denis Villemonais.
  
• Large deviations principle for a stochastic process with random reinforced relocations (31 pages)
  Erion-Stelios Boci and Cécile Mailler.
  
• Voronoi cells in random split trees (25 pages)
  Alexander Drewitz, Markus Heydenreich and Cécile Mailler.
  

Journal Publications

• Parametrised branching processes: a functional version of Kesten and Stigum's theorem (40 pages)
  Cécile Mailler and Jean-François Marckert.
  Stochastic Processes and their Applications, Volume 152, pages 339-377, 2022.
  
• The trace-reinforced ants process does not find shortest paths. (26 pages)
  Daniel Kious, Cécile Mailler and Bruno Schapira.
  Journal de l'École Polytechnique, Tome 9, pages 505-538, 2022.
  A [video] of a 1-hour talk on this pre-print.
  
• Finding geodesics on graphs using reinforcement learning (39 pages)
  Daniel Kious, Cécile Mailler and Bruno Schapira.
  Annals of Applied Probability (accepted for publication).
  A [video] of a 1-hour talk on this paper.
  
• Dynamical models for random simplicial complexes (45 pages)
  Nikolaos Fountoulakis, Tejas Iyer, Cécile Mailler and Henning Sulzbach.
  Annals of Applied Probability Annals of Applied Probability, Volume 32, No. 4, pp 2860-2913, 2022.
  
• Strict monotonic trees arising from evolutionary processes: combinatorial and probabilistic study (45 pages)
  Olivier Bodini, Antoine Genitrini, Cécile Mailler and Mehdi Naima.
  Advances in Applied Mathematics, Volume 133, 102284, February 2022.
  
• Competing growth processes with random growth rates and random birth times (36 pages)
  Cécile Mailler, Peter Mörters and Anna Senkevich.
  Stochastic Processes and their Applications, 135, pp 183-226, 2021.
  
• Stochastic approximation on non-compact measure spaces and application to measure-valued Pólya processes. (46 pages)
  Cécile Mailler and Denis Villemonais.
  Annals of Applied Probability, 30(5), pp 2393-2438, 2020.
  
• Characterising random partitions by random colouring (12 pages)
  Jakob E. Björnberg, Cécile Mailler, Peter Mörters and Daniel Ueltschi.
  Electronic Communications in Probability, Volume 25, paper no. 4, 12 pp, 2020.
  
• Unbiased on-lattice domain growth. (15 pages)
  Cameron Smith, Cécile Mailler and Kit Yates.
  Physical Review E, 100(6), pp 063307, 2019.
  
• Random walks with preferential relocations and fading memory: a study through random recursive trees. (35 pages)
  Cécile Mailler and Gerónimo Uribe Bravo.
  Journal of Statistical Mechanics: Theory and Experiment, September 2019.
  
• Multiple drawing multi-colour urns by stochastic approximation. (20 pages)
  Nabil Lasmar, Cécile Mailler and Olfa Selmi.
  Journal of Applied Probability, 55(1), pp 254-281, 2018.
  
• Describing the asymptotic behaviour of multicolour Pólya urns via smoothing systems analysis. (26 pages)
  Cécile Mailler.
  Latin American Journal of Probability and Mathematical Statistics - ALEA, XV, pp 375-408, 2018.
  
• And/or trees: a local limit point of view. (33 pages)
  Nicolas Broutin and Cécile Mailler.
  Random Structures and Algorithms, 53(1), pp 15-58, 2018.
  
• Measure-valued Pólya processes. (37 pages)
  Cécile Mailler and Jean-François Marckert.
  Electronic Journal of Probability 22, paper no. 26, pp 33 (DOI:10.1214/17-EJP47), 2017.
  I gave a talk on this work at the Workshop on Analytic and Probabilistic Combinatorics at BIRS (Banff, Canada); the video of this talk is available here.
  
• Non extensive condensation in reinforced branching processes. (20 pages)
  Steffen Dereich, Cécile Mailler and Peter Mörters.
  Annals of Applied Probability 27(4), pp 2539-2568, 2017.
  
• A bijective study of Basketball walks. (20 pages)
  Jérémie Bettinelli, Éric Fusy, Cécile Mailler and Lucas Randazzo.
  Séminaire Lotharingien de Combinatoire, 77, Art. B77a, pp 1–24, 2017.
  
• The relation between tree size complexity and probability for Boolean functions generated by uniform random trees. (22 pages)
  Antoine Genitrini, Bernhard Gittenberger, Veronika Kraus and Cécile Mailler.
  Applicable Analysis and Discrete Mathematics, Volume 10(2), pp 408-446 (DOI 10.2298/AADM160715015D), 2016.
  
• Condensation and symmetry-breaking in the zero-range process with weak site disorder. (22 pages)
  Cécile Mailler, Peter Mörters and Daniel Ueltschi.
  Stochastic Processes and their Applications 126(11), pp 3283-3309 (DOI 10.1016/j.spa.2016.04.028), 2016.
  
• Generalised and Quotient Models for Random And/Or Trees and Application to Satisfiability. (23 pages)
  Antoine Genitrini et Cécile Mailler.
  Algorithmica 76(4), pp 1106-1138, 2016.
  
• Associative and commutative tree representations for Boolean functions. (36 pages)
  Antoine Genitrini, Bernhard Gittenberger, Veronika Kraus and Cécile Mailler.
  Theoretical Computer Science, 570, pp 70-101 (DOI : 10.1016/j.tcs.2014.12.025), 2015.
  
• A sprouting tree model for random Boolean functions. (23 pages)
  Brigitte Chauvin, Danièle Gardy and Cécile Mailler.
  Random Structures and Algorithms, 47(4), page 635, 2015.
  
• Smoothing equations for large Pólya urns. (26 pages)
  Brigitte Chauvin, Cécile Mailler and Nicolas Pouyanne.
  Journal of Theoretical Probability, 28, pages 923-957, 2015.
  
• Probabilities of Boolean functions given by random implicational formulas. (20 pages)
  Antoine Genitrini, Bernhard Gittenberger, Veronika Kraus and Cécile Mailler.
  Electronic Journal of Combinatorics, 19, No. 2, P37 (electronic), 2012.
  

Articles in conference proceedings

• The Disordered Chinese Restaurant and Other Competing Growth Processes.
  Cécile Mailler, Peter Mörters and Anna Senkevich.
  In proc. 31st International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA'20), LIPIcs 21:1-21:13, 2020.
  
• No Shannon effect induced by And/Or trees.
  Antoine Genitrini, Bernhard Gittenberger and Cécile Mailler.
  In proc. 25th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA'14), DMTCS, pages 109-120, 2014.
  
• Equivalence classes of random Boolean trees and application to the Catalan satisfiability problem.
  Antoine Genitrini and Cécile Mailler.
  In proc. 11^th Latin American Theoretical INformatics Symposium (LATIN), LNCS volume 8392, pages 466-477, 2014.
  
• The growing tree distribution for Boolean functions.
  Brigitte Chauvin, Danièle Gardy and Cécile Mailler.
  In proc. 8^th SIAM Workshop on Analytic and Combinatorics (ANALCO), pages 45-56, 2011.
  

PhD Thesis

• Random Boolean Trees and Pólya Urns: Combinatorial and Probabilistic Approaches.
  Defended on October 17^th, 2013.

Teaching at summer schools

• Mini-course on Pólya urns at the Journées Aléa 2019, CIRM, Luminy, France, March 18th-22nd 2019. [slides - in French]
  
• Mini-course on Reinforced Branching Processes at the Alea-Network Young Researchers' Workshop, 6th-9th September 2016. [lecture notes]
  
• Course on Markov Chains and Martingales for the Analysis of Discrete Random Structures at the CIMPA summer school Random structures, Analytic and Probabilistic Approaches, 2014, Nablus. [lecture notes]
• Exercises sessions of Brigitte Chauvin's course "Random trees for analysis of algorithms" at the BMS Summer School 2011 -- 2011, Berlin.

Selected recent talks

The ants walk: finding geodesics in a graph using reinforcement learning.

• Workshop "Stochastic processes under constraints", Oberwolfach (online), October 1st, 2020.
• Séminaire de Probabilités de l'Université de Lille, online, September 23rd, 2020.

Study of extremes in three competing growth processes.

• Bernoulli-IMS One World Symposium, online, August, 2020.

Dynamical models for random simplices.

• Durham probability seminar, online, April 27, 2020.
• Research Seminar of the Research Training Group "High-dimensional Phenomena in Probability - Fluctuations and Discontinuity", University of Duisburg-Essen (online), May 4th, 2020.

Stochastic approximation on a non-compact space and application to measure-valued Pólya processes.

• King's college probability seminar, London, UK, September 23, 2019.
• Rencontre ANR/SNSF MALIN, Les Diablerets, Switzerland, June 10th-14th 2019.
• UK Easter Probability meeting, Sheffield, April, 2018.

The monkey walk: a random walk with random reinforced relocations.

• Séminaire Philippe Flajolet, IHP, Paris, France, June 6, 2019.
• Workshop "Women in Probability" 2019, Technical University of Munich, Germany, May 31th-June 1st 2019.
• SPA 2019, Northwestern University, Chicago, USA, July 8th-12th 2019.
• King's college workshop on random graphs and random processes, King's college, London, April 9th 2019.
• Zurich's seminar on stochastic processes, Zurich, October, 2018.
• 672. WE-Heraeus Seminar "Search and Problem Solving by Random Walks", Bad Honnef, Germany, May, 2018.

PhD students

• Chris Dean (2020-): Pólya urns with growing initial composition.
• Stelios Boci (2018-): Large deviations for the Monkey walk.
• Anna Senkevich (2016-2019): Competing growth processes with random growth rates and random birth times. (Co-supervised with Peter Mörters)

My résumé