Bang--Bang Principle

Oriented measures with continuous densities and the bang–bang principle, with C. Mariconda, J. Funct. Anal. 126 (1994), 476–505. PDF.

On bang–bang solutions of a control system, with C. Mariconda, S.I.A.M. Jour. Control and Optimization 33 (1995), 554–567. PDF.

Oriented measures, with C. Mariconda, Jour. Math. Anal. Appl. 197 (1996), 925–944. PDF.

Chebyshev measures, with C. Mariconda, Proc. Amer. Math. Soc. 125 (1997), 3321–3329. PDF.

Two dimensional zonoids and Chebyshev measures, with S. Bianchini and C. Mariconda, Jour. Math. Anal. Appl. 211 (1997), 512–526. PDF.

Genetic
Algorithms

The dynamics of mutation–selection algorithms with large population sizes, Ann. Inst. Henri Poincaré 32 no.4 (1996), 455–508. PDF.

A new genetic algorithm, Annals of Applied Probab. 3 (1996), 778–817. PDF.

Asymptotic convergence of genetic algorithms, Adv. Appl. Prob. 30 (1998), 521–550. PDF.

Critical control of a genetic algorithm, preprint (2010). PDF.

The quasispecies regime for the simple genetic algorithm with ranking selection, Trans. Amer. Math. Soc. 369 (2017), 6017-6071. PDF

The quasispecies regime for the simple genetic algorithm with roulette-wheel selection, Adv. Appl. Prob. 49 (2017), 903-926. PDF

Quasispecies

Critical population and error threshold on the sharp peak landscape for the Wright-Fisher model, Ann. Applied Probab. 25 no. 4 (2015), 1936–1992. PDF.

The distribution of the quasispecies for a Moran model on the sharp peak landscape, with J. Dalmau, Stochastic Processes and Applications 126(6):1681-1709 (2016). PDF

Quasispecies on class-dependent fitness landscapes, with J. Dalmau, Bulletin of Mathematical Biology 78(6):1238-1258 (2016). PDF

A Markov chain representation of the Perron-Frobenius eigenvector, with J. Dalmau, Electronic Comm. Probab. 22, paper no. 52 (2017). PDF

The quasispecies for the Wright–Fisher model, with J. Dalmau, Journal of Evolutionary Biology 45:318-323 (2018). PDF.

A probabilistic proof of Perron's theorem, with J. Dalmau, RMS 130 no. 2, 3-10 (2020)

A basic model of mutations, with M. Berger, preprint (2018). PDF.

Galton-Watson and branching process representations of the normalized Perron-Frobenius eigenvector, with J. Dalmau, ESAIM Probab. Stat. 23 (2019), 797-802. PDF.

The quasispecies distribution, with J. Dalmau, preprint (2016). PDF

The quasispecies equation, with J. Dalmau, in preparation (2020). PDF

Metastability

The three dimensional polyominoes of minimal area, with L. Alonso, Electronic Journal of Combinatorics 3 #R27 (1996). PDF.

Metastability of the three dimensional Ising model on a torus at very low temperatures, with G. Ben Arous, Electronic Journal of Probability 1 (1996), 1–55. PDF.

The exit path of a Markov chain with rare transitions, with O. Catoni, ESAIM:P&S 1 (1996), 95–144. PDF.

A d dimensional nucleation and growth model, with F. Manzo, Probab. Theory and Related Fields 155 no. 1-2 (2013), 427-449. PDF.

Nucleation and growth for the Ising model in d dimensions at very low temperatures, with F. Manzo, Ann. Probab. 41 no.6 (2013), 3697-3785. PDF

Mean curvature motion

The initial drift of a 2D droplet at zero temperature, with S. Louhichi, Probab. Theory and Related Fields 137 (2007), 379–428. PDF.

Wulff
crystal

Large deviations for i.i.d. random compact sets, Proc. Amer. Math. Soc. 127 (1999), 2431–2436. PDF.

On the Wulff crystal in the Ising model, with A. Pisztora, Ann. Probab. 28 no.3 (2000), 945–1015. PDF.

Phase coexistence in Ising, Potts and percolation models, with A. Pisztora, Ann. Inst. H. Poincaré Probab. Statist. 37 no. 6 (2001), 643–724. PDF.

The low temperature expansion of the Wulff crystal in the 3D Ising model, with R. Kenyon, Comm. Math. Phys. 222 no.1 (2001), 147–179. PDF.

The Wulff crystal in Ising and Percolation models, Lecture notes in Mathematics 1878, 264 pages, Springer-Verlag, 2006. PS with pictures. PS without pictures.

On the 2D Ising Wulff crystal near criticality, with R. Messikh, Ann. Probab. 38 no.1 (2010), 102-149. PDF.

Perimeter

The Hausdorff lower semicontinuous envelope of the length in the plane, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) I (2002), 33–71. PDF.

Bernoulli percolation

Large deviations of the finite cluster shape for two–dimensional percolation in the Hausdorff and L1 metric, Journal of Theoretical Probability 13 no.2 (2000), 491-518. PDF.

Large deviations for three dimensional supercritical percolation, Astérisque 267, 177 pages, Société Mathématique de France, 2000. PS.

A lower bound on the two-arms exponent for critical percolation on the lattice, Ann. Probab. 43 no.5 (2015), 2458-2480. PDF.

The travel time in a finite box in supercritical Bernoulli percolation, Electronic Communications in Probability 19 article 21 (2014). PDF.

Bootstrap percolation

Finite size scaling in three dimensional bootstrap percolation, with E. Cirillo, Annals of Probab. 27 no.4 (1999), 1837–1850. PDF.

The threshold regime of finite volume bootstrap percolation, with F. Manzo, Stochastic Process. Appl. 101 (2002), 69–82. PDF.

First passage percolation

Upper large deviations for the maximal flow through a domain of Rd in first passage percolation, with M. Théret, Annals Applied Probability 21 no. 6 (2011), 2075–2108. PDF.

Lower large deviations for the maximal flow through a domain of Rd in first passage percolation, with M. Théret, Probab. Theory and Related Fields 150 no. 3 (2011), 635–661. PDF.

Law of large numbers for the maximal flow through a domain of Rd in first passage percolation, with M. Théret, Transactions of the American Mathematical Society 363 no. 7 (2011), 3665-3702. PDF.

Maximal stream and minimal cutset for first passage percolation through a domain of Rd, with M. Théret, Annals of Probability 42, no 3 (2014), 1054-1120. PDF.

Weak shape theorem in first passage percolation with infinite passage times, with M. Théret, Ann. Inst. Henri Poincaré 52 no.3 (2016), 1351-1381. PDF.

Cramér's theory

On Cramér theory in infinite dimensions, Panoramas et Synthèses, 159 pages, vol. 23, Société Mathématique de France, 2007. PDF.

A short proof of Cramér’s theorem, with P. Petit, American Mathematical Monthly 118 no. 10 (2011), 925–931. PDF.

Cramér’s theorem for asymptotically decoupled ﬁelds, with P. Petit, preprint (2011). PDF.

Self-organized criticality

A Curie-Weiss Model of Self-Organized Criticality, with M. Gorny, Annals of Probability 44 no. 1 (2016), 444-478. PDF.

Curious inequalities

A Lower Bound on the Relative Entropy with Respect to a Symmetric Probability, with M. Gorny, Electronic Communications in Probability 20 article 5 (2015). PDF.

An Exponential Inequality for Symmetric Random Variables, with M. Gorny, American Mathematical Monthly 122 No. 8 (October 2015), 786-789. PDF.