The exit path of a Markov chain with rare transitions
ESAIM: Probability and Statistics, Tome 1 (1997), pp. 95-144.
@article{PS_1997__1__95_0,
     author = {Catoni, Olivier and Cerf, Rapha\"el},
     title = {The exit path of a {Markov} chain with rare transitions},
     journal = {ESAIM: Probability and Statistics},
     pages = {95--144},
     publisher = {EDP-Sciences},
     volume = {1},
     year = {1997},
     zbl = {0869.60063},
     mrnumber = {1440079},
     language = {en},
     url = {http://www.numdam.org/item/PS_1997__1__95_0/}
}
TY  - JOUR
AU  - Catoni, Olivier
AU  - Cerf, Raphaël
TI  - The exit path of a Markov chain with rare transitions
JO  - ESAIM: Probability and Statistics
PY  - 1997
DA  - 1997///
SP  - 95
EP  - 144
VL  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/PS_1997__1__95_0/
UR  - https://zbmath.org/?q=an%3A0869.60063
UR  - https://www.ams.org/mathscinet-getitem?mr=1440079
LA  - en
ID  - PS_1997__1__95_0
ER  - 
Catoni, Olivier; Cerf, Raphaël. The exit path of a Markov chain with rare transitions. ESAIM: Probability and Statistics, Tome 1 (1997), pp. 95-144. http://www.numdam.org/item/PS_1997__1__95_0/

Alonso, L. and Cerf, R. ( 1996), The three dimensional polyominoes of minimal area, Electronic Journal of Combinatorics 3 # R27. | MR 1410882 | Zbl 0885.05056

Ben Arous, G. and Cerf, R. ( 1996), Metastability of the three dimensional Ising model on a torus at very low temperatures, Electronic Journal of Probability 1 1-55. | MR 1423463 | Zbl 0888.60057

Cassandro, M., Galves, A., Olivieri, E. and Vares, M.E. ( 1984), Metastable behaviour of stochastic dynamics: a pathwise approach, Jour. Stat. Phys. 35 nos. 5/6 603-634. | MR 749840 | Zbl 0591.60080

Catoni, O. ( 1988), Grandes déviations et décroissance de la température dans les algorithmes de recuit, C.R. Acad. Sci. Paris Sér. 1 307 535-538. | MR 966258 | Zbl 0645.60035

Catoni, O. ( 1990), Large deviations for annealing, PhD Thesis, University Paris XI.

Catoni, O. ( 1991a), Sharp large deviation estimates for simulated annealing algorithms, Ann. Inst. Henri Poincaré Vol. 27 no. 3 291-383. | Numdam | MR 1131838 | Zbl 0746.60024

Catoni, O. ( 1991b), Applications of Sharp Large Deviation Estimates to Optimal Cooling Schedules, Ann. Inst. Henri Poincaré 27 463-518. | Numdam | MR 1141244 | Zbl 0752.60025

Catoni, O. ( 1992), Rough large deviation estimates for simulated annealing. Application to exponential schedules, Annals of Probab. 20 1109-1146. | MR 1175253 | Zbl 0755.60021

Catoni, O. ( 1994), The energy transformation method for the Metropolis algorithm compared with simulated annealing, Probab. Theory and Rel. Fields (to appear). | MR 1602040 | Zbl 0897.60078

Catoni, O. ( 1995), Algorithmes de recuit simulé et chaînes de Markov à transitions rares. Notes de cours de DEA, English translation: Simulated Annealing Algorithms and Markov Chains with Rare Transitions ( 1996), Université Paris 11, lecture notes, DEA Stochastic Models and Statistics.

Catoni, O. and Cot, C. ( 1996), Rate of Convergence of Generalized Simulated Annealing with Piecewise Constant Triangular Cooling Schedules, preprint Rapport de Recherche du L.M.E.N.S..

Cerf, R. ( 1993), Asymptotic convergence of genetic algorithms, preprint. | MR 1642852 | Zbl 0805.60019

Cerf, R. ( 1994), Une théorie asymptotique des algorithmes génétiques, PhD Thesis, Université Montpellier II.

Cerf, R. ( 1996a), An asymptotic theory for genetic algorithms, Artificial Evolution, Lecture Notes in Computer Science 1063, Springer-Verlag, 37-53.

Cerf, R. ( 1996b), The dynamics of mutation-selection algorithms with large population sizes, Ann. Inst. Henri Poincaré 32 no. 4 455-508. | EuDML 77543 | Numdam | MR 1411269 | Zbl 0861.60038

Cerf, R. ( 1996c), A new genetic algorithm, Annals Applied Probab. Vol. 6 no. 3 778-817. | MR 1410116 | Zbl 0860.60017

Chen, D., Feng, J. and Qian, M. ( 1995), The Metastability of Exponentially Perturbed Markov Chains, Chinese Science A 25(6) 590-595. | MR 1397231

Chiang, T.S. and Chow, Y. ( 1989), A Limit Theorem for a Class of Inhomogeneous Markov Processes, Annals of Probab. 17 no 4 1483-1502. | MR 1048941 | Zbl 0687.60070

Chiang, T.S. and Chow, Y. ( 1995), On the Exit Problem from a Cycle of Simulated Annealing Processes, Tech. Rept. Inst. of Math. Academia Sinica. | MR 1335464

Diaconis, P. and Stroock, D. ( 1991), Geometric bounds for eigenvalues of Markov chains, Annals Applied Probab. Vol. 1 no. 1 36-61. | MR 1097463 | Zbl 0731.60061

Deuschel, J.D. and Mazza, C. ( 1994), L2 convergence of time nonhomogeneous Markov processes: I. Spectral Estimates, Annals Applied Probab. Vol. 4 no. 4 1012-1056. | MR 1304771 | Zbl 0819.60063

Freidlin, M.I. and Wentzell, A.D. ( 1984), Random perturbations of dynamical systems, Springer-Verlag, New York. | MR 722136 | Zbl 0522.60055

Götze, F. ( 1991), Rate of Convergence of Simulated Annealing Processes, preprint. | MR 1106283

Holley, R. and Stroock, D.W. ( 1988), Simulated Annealing via Sobolev Inequalities, Commun. Math. Phys. Vol. 115 553-569. | MR 933455 | Zbl 0643.60092

Holley, R., Kusuoka, S. and Stroock, D. ( 1989), Asymptotics of the Spectral Gap with Applications to the Theory of Simulated Annealing, J. Funct. Anal. 83 333-347. | MR 995752 | Zbl 0706.58075

Hwang, C.R. and Sheu, S.J. ( 1986), Large Time Behaviors of Perturbed Diffusion Markov Processes with Applications III Simulated Annealing, preprint, cited in Chiang and Chow ( 1989). | MR 854657

Hwang, C.R. and Sheu, S.J. ( 1992), Singular perturbed Markov chains and exact behaviour of simulated annealing processes, J. Theoret. Prob. Vol. 5 no. 2 223-249. | MR 1157983 | Zbl 0755.60047

Kotecky, R. and Olivieri, E. ( 1993), Droplet dynamics for asymmetric Ising model, Jour. Stat. Phys. 70 nos. 5/6 1121-1148. | MR 1208633 | Zbl 1081.82591

Kotecky, R. and Olivieri, E. ( 1994), Shapes of growing droplets - a model of escape from a metastable phase, Jour. Stat. Phys. 75 nos 3/4 409-506. | MR 1279759 | Zbl 0831.60103

Mlclo, L. ( 1991), Evolution de l'énergie libre. Application à l'étude de la convergence des algorithmes de recuit simulé, Thèse, Université Paris XI-Orsay.

Mlclo, L. ( 1995), Sur les temps d'occupations des processus de Markov finis inhomogènes à basse température, preprint, submitted to Stochastics and Stochastics Reports. | MR 1639780 | Zbl 1002.60565

Mlclo, L. ( 1996), Sur les problèmes de sortie discrets inhomogène, Annals Applied Probab. (to appear). | MR 1422980 | Zbl 0870.60062

Neves, E.J. and Schonmann, R.H. ( 1991), Critical droplets and metastability for a Glauber dynamics at very low temperatures, Commun. Math. Phys. 137 209-230. | MR 1101685 | Zbl 0722.60107

Neves, E.J. and Schonmann, R.H. ( 1992), Behaviour of droplets for a class of Glauber dynamics at very low temperatures, Prob. Th. Related Fields 91 331-354. | MR 1151800 | Zbl 0739.60101

Olivieri, E. and Scoppola, E. ( 1995), Markov chains with exponentially small transition probabilities: first exit problem from a general domain -I. The reversible case, Journ. Stat. Phys. 79 613-647. | MR 1327899 | Zbl 1081.60541

Olivieri, E. and Scoppola, E. ( 1996), Markov chains with exponentially small transition probabilities: first exit problem from a general domain -II. The general case, Journ. Stat. Phys. (to appear). | MR 1412076 | Zbl 1081.60542

Schonmann, R.H. ( 1992), The pattern of escape from metastability of a stochastic Ising model, Commun. Math. Phys 147 231-240. | MR 1174411 | Zbl 0755.60093

Scoppola, E. ( 1993), Renormalization group for Markov chains: a general procedure based on renormalization group ideas, Jour. Stat. Phys. 73 nos. 1/2 83-121. | MR 1247859 | Zbl 1101.82330

Trouvé, A. ( 1992), Convergence optimale pour les algorithmes de recuits généralisés. C. R. Acad. Sci. Paris t.315 Série I 1197-1202. | MR 1194517 | Zbl 0776.60088

Trouvé, A. (january 1993), Parallélisation massive du recuit simulé, PhD Thesis, University Paris XI.

Trouvé A. ( 1996a), Cycle decompositions and simulated annealing, SIAM J. Control Optimization 34 no. 3 966-986. | MR 1384962 | Zbl 0852.60031

Trouvé, A. ( 1996b), Rough large deviation estimates for the optimal convergence speed exponent of generalized simulated annealing algorithms, Ann. Inst. Henri Poincaré 32 no. 3 299-348. | EuDML 77537 | Numdam | MR 1387393 | Zbl 0853.60029

Tsitsiklis, J.N. ( 1989), Markov Chains with Rare Transitions and Simulated Annealing, Math. Oper. Res. 14 70-90. | MR 984559 | Zbl 0664.60067