List of Publications. Roberto H. Schonmann

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List of Publications Roberto H. Schonmann (1) J.F.Perez, R.H.Schonmann: On the global character of some local equilibrium conditions - a remark on metastability. Journal of Statistical Physics 28, 479-485 (1982). (2) R.H.Schonmann: Metastability for the contact process. Journal of Statistical Physics 41, 445-464 (1985). (3) R.H.Schonmann: Central limit theorem for the contact process. The Annals of Probability 14, 1291-1295 (1986). (4) R.H.Schonmann, M.E.Vares: The survival of the large dimensional basic contact process. Probability Theory and Related Fields 72, 387-393 (1986). (5) R.H.Schonmann: A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter. The Annals of Probability 15, 382-387 (1987). (6) R.H.Schonmann: Absence of a stationary distribution for the edge process of subcritical oriented percolation in two dimensions. The Annals of Probability 15, 1146-1147 (1987). (7) R.H.Schonmann: The asymmetric contact process. Journal of Statistical Physics 44, 505-534 (1986). (8) J.L.Lebowitz, R.H.Schonmann: Pseudo free energies and large deviations for non-gibbsian FKG measures. Probability Theory and Related Fields 77, 49-64 (1988). (9) R.Durrett, R.H.Schonmann: Stochastic growth models. in Percolation Theory and Ergodic Theory of Infinite Particle Systems. The IMA volumes in mathematics and its applications, vol. 8, H.Kesten, ed. (Springer Verlag, 1987), pp. 85-119. (10) R.H.Schonmann: A new look at contact processes in several dimensions. in Percolation Theory and Ergodic Theory of Infinite Particle Systems. The IMA volumes in mathematics and its applications, vol. 8, H.Kesten, ed. (Springer Verlag, 1987), pp. 245-250. (11) M.Bramson, P.Calderoni, A. DeMasi, P.A.Ferrari, J.L.Lebowitz, R.H.Schonmann: Microscopic selection principle for reaction diffusion equation. Journal of Statistical Physics 45, 905-920 (1986). (12) J.L.Lebowitz, R.H.Schonmann: On the asymptotics of occurrence times of rare events for stochastic spin systems. Journal of Statistical Physics 48, 727-751 (1987). (13) R.Durrett, R.H.Schonmann: The contact process on a finite set II. The Annals of Probability16, 1570-1583 (1988). (14) R.Durrett, R.H.Schonmann: Large deviations for the contact process and two dimensional percolation. Probability Theory and Related Fields 77, 583-603 (1988). (15) R.H.Schonmann: Second order large deviation estimates for ferromagnetic systems in the phase coexistence region. Communications in Mathematical Physics 1

2 R.H.SCHONMANN 112, 409-422 (1987). (16) J.T.Chayes, L.Chayes, R.H.Schonmann: Exponential decay of connectivities in the two dimensional Ising model. Journal of Statistical Physics 49, 433-445 (1987). (17) R.H.Schonmann: Projections of Gibbs measures may be non-gibbsian. Communications in Mathematical Physics 124, 1-7 (1989). (18) J.T.Chayes, L.Chayes, G.Grimmett, H.Kesten, R.H.Schonmann: The correlation length of the high density phase of Bernoulli percolation. The Annals of Probability 17, 1277-1302 (1989). (19) R.H.Schonmann: Exponential convergence under mixing. Probability Theory and Related Fields 81, 235-238 (1989). (20) R.H.Schonmann: On two correlation inequalities for Potts models. Journal of Statistical Physics 52, 61-67 (1988). (21) R.Durrett, R.H.Schonmann, N.I.Tanaka: The contact process on a finite set III. The critical case. The Annals of Probability 17, 1303-1321 (1989). (22) R.Durrett, R.H.Schonmann, N.I.Tanaka: Correlation lengths for oriented percolation. Journal of Statistical Physics 55, 965-979 (1989). (23) J.Bricmont, H.Kesten, J.L.Lebowitz, R.H.Schonmann: A note on the large dimensional Ising model. Communications in Mathematical Physics 122, 597-607 (1989). (24) H.Kesten, R.H.Schonmann: Behavior in high dimensions of Potts and Heisenberg models. Reviews in Mathematical Physics 1, 147-182 (1990). (25) M.Bramson, R.Durrett, R.H.Schonmann: The contact process in a random environment. The Annals of Probability 19, 960-983 (1991). (26) E.D.Andjel, R.B.Schinazi, R.H.Schonmann: Edge processes of one dimensional stochastic growth models. Ann. inst. H. Poincaré, Sect B (Probab. and Statist.) 26, 489-506 (1990). (27) R.H.Schonmann: On the behavior of some cellular automata related to bootstrap percolation. The Annals of Probability 20, 174-193 (1992). (28) E.J.Neves, R.H.Schonmann: Critical droplets and metastability for a Glauber dynamics at very low temperatures. Communications in Mathematical Physics 137 209-230 (1991). (29) R.H.Schonmann: Critical points of two-dimensional bootstrap percolation like cellular automata. Journal of Statistical Physics 58, 1239-1244 (1990). (30) R.H.Schonmann, N.I.Tanaka: One-dimensional caricature of phase transition. Journal of Statistical Physics 61, 241-252 (1990). Errata published in Journal of Statistical Physics 64, 477 (1991). (31) E.J.Neves, R.H.Schonmann: Behavior of droplets for a class of Glauber dynamics at very low temperature. Probability Theory and Related Fields 91, 331-354 (1992). (32) R.H.Schonmann: Finite size scaling behavior of a biased majority rule cellular automaton. Physica A 167, 619-627 (1990). (33) R.H.Schonmann: An approach to characterize metastability and critical droplets in stochastic Ising models. Ann. inst. H. Poincaré, Sect A (Phys. Théor.) 55 591-600 (1991).

R.H.SCHONMANN 3 (34) P.A.Ferrari, A.Frigessi, R.H.Schonmann: Convergence of some partially parallel Gibbs samplers with annealing. The Annals of Applied Probability 3 137-153 (1993). (35) R.H.Schonmann: The pattern of escape from metastability of a stochastic Ising model. Communications in Mathematical Physics 147 231-240 (1992). (36) E.D.Andjel, T.S.Mountford, R.H.Schonmann: Equivalence of exponential decay rates for bootstrap-percolation-like cellular automata. Ann. inst. H. Poincaré, Sect B (Probab. and Statist.) 31 13-25 (1995). (37) N.Madras, R.B.Schinazi, R.H.Schonmann: On the critical behavior of the contact process in deterministic inhomogeneous environment. The Annals of Probability 22 1140-1159 (1994). (38) R.H.Schonmann: Relaxation times for stochastic Ising models in the limit of vanishing external field at fixed low temperatures. in Cellular Automata and Cooperative Systems. NATO ASI Series. Series C: Mathematical and Physical Sciences - Vol.396. N.Boccara, E.Goles, S.Martinez and P.Picco, eds. (Kluwer Academic Publisher, 1993), pp. 543-546. (39) R.H.Schonmann: Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region. Communications in Mathematical Physics 161 1-50 (1994). (40) F.Martinelli, E.Olivieri, R.H.Schonmann: For 2-D lattice spin systems weak mixing implies strong mixing. Communications in Mathematical Physics 165 33-47 (1994). (41) R.H.Schonmann: Theorems and conjectures on the droplet-driven relaxation of stochastic Ising models. in Probability and Phase Transition. NATO ASI Series. Series C: Mathematical and Physical Sciences - Vol.420. G. Grimmett, ed. (Kluwer Academic Publisher, 1994), pp. 265-301. (42) H.Kesten, R.H.Schonmann: On some growth models with a small parameter. Probability Theory and Related Fields 101 435-468 (1995). (43) R.H.Schonmann, S.B.Shlosman: Complete analyticity for 2D Ising completed. Communications in Mathematical Physics 170 453-482 (1995). (44) L.Chayes, R.H.Schonmann, G.Swindle: Lifshitz law for the volume of a twodimensional droplet at zero temperature. Journal of Statistical Physics 79 821-831 (1995). (45) R.H.Schonmann, S.B.Shlosman: Constrained variational problem with applications to the Ising model. Journal of Statistical Physics 83 867-905 (1996). (46) F. Cesi, G. Guadagni, F. Martinelli, R.H.Schonmann: On the 2D dynamical Ising model in the phase coexistence region near the critical point. Journal of Statistical Physics 85 55-102 (1996). (47) T.M.Liggett, R.H.Schonmann, A.Stacey: Domination by product measures. The Annals of Probability 25 71-95 (1997). (48) R.H.Schonmann, N. Yoshida: Exponential relaxation of Glauber dynamics with some special boundary conditions. Communications in Mathematical Physics 189 299-309 (1997). (49) P.Dehghanpour, R.H.Schonmann: A nucleation-and-growth model. Probability Theory and Related Fields 107 123-135 (1997).

4 R.H.SCHONMANN (50) M.Salzano, R.H.Schonmann: The second lowest extremal invariant measure of the contact process. The Annals of Probability 25 1846-1871 (1997). (51) P.Dehghanpour, R.H.Schonmann: Metropolis dynamics relaxation via nucleation and growth. Communications in Mathematical Physics 188 89-119 (1997). (52) A.C.D.van Enter, R.Fernández, R.H.Schonmann, S.B.Shlosman: Complete analyticity of the 2D Potts model above the critical temperature. Communications in Mathematical Physics 189 373-393 (1997). (53) R.H.Schonmann, N.I.Tanaka: Lack of monotonicity in ferromagnetic Ising model phase diagrams. The Annals of Applied Probability 8 234-245 (1998). (54) R.H.Schonmann, S.B.Shlosman: Wulff droplets and the metastable relaxation of kinetic Ising models. Communications in Mathematical Physics 194 389-462 (1998). (55) M.Salzano, R.H.Schonmann: A new proof that for the contact process on homogeneous trees local survival implies complete convergence. The Annals of Probability 26 1251-1258 (1998). (56) R.H.Schonmann: The triangle condition for contact processes on homogeneous trees. Journal of Statistical Physics 90 1429-1440 (1998). (57) D.Ioffe, R.H.Schonmann: Dobrushin-Kotecký-Shlosman theorem up to the critical temperature. Communications in Mathematical Physics 199 117-167 (1998). (58) M.Salzano, R.H.Schonmann: The second lowest extremal invariant measure of the contact process II. The Annals of Probability 27 845 875 (1999) (59) E.Kira, E.J.Neves, R.H.Schonmann: A Note on Percolation in a Voronoi Competition Growth Model. Journal of Statistical Physics 92 755-764 (1998). (60) R.H.Schonmann: Stability of infinite clusters in supercritical percolation. Probability Theory and Related Fields 113 287 300 (1999). (61) R.H.Schonmann: Metastability and the Ising model. in Proceedings of the International Congress of Mathematicians, Berlin 1998, Vol. III. G.Fischer, U.Rehmann, eds. (Documenta Mathematica, Extra Volumes, 1998), pp. 173-181. (62) R.H.Schonmann: Percolation in + 1 dimensions at the uniqueness threshold. in Perplexing Problems in Probability. Festschrift in honor of Harry Kesten. M. Bramson, R. Durrett, ed. (Birkhäuser, 1999), pp. 53-67. (63) O.Häggström, Y.Peres and R.H.Schonmann: Percolation on transitive graphs as a coalescent process: relentless merging followed by simultaneous uniqueness. in Perplexing Problems in Probability. Festschrift in honor of Harry Kesten. M. Bramson, R. Durrett, ed. (Birkhäuser, 1999), pp. 69-90. (64) A. van Enter, C. Maes, R.H.Schonmann and S. Shlosman: The Griffiths singularity random field. in On Dobrushin s way: from probability theory to statistical physics. R. Minlos, S. Shlosman, Y. Sukhov, ed. (AMS, 2000), pp. 51-58. (65) O. Häggström, R.H.Schonmann and J. E. Steif: The Ising model on diluted graphs and strong amenability. The Annals of Probability 28 1111 1137 (2000). (66) L. Chayes and R.H.Schonmann: Mixed percolation as a bridge between site and bond percolation. The Annals of Applied Probability 10 1182 1196 (2000). (67) R.H.Schonmann: Multiplicity of phase transitions and mean-field criticality on highly non-amenable graphs. Communications in Mathematical Physics 219 271 322 (2001).

R.H.SCHONMANN 5 (68) P. Bleher, J. Ruiz, R.H.Schonmann, S. Shlosman and V. Zagrebnov: Rigidity of the critical phases on a Cayley tree. Moskow Mathematical Journal 1 345 363 (2001). (69) R.H.Schonmann: Mean-field criticality for percolation on planar non-amenable graphs. Communications in Mathematical Physics 225 453 463 (2002). (70) L. R. Fontes, R.H.Schonmann and V. Sidoravicius: Stretched exponential fixation in stochastic Ising models at zero temperature. Communications in Mathematical Physics 228 495 518 (2002). (71) R.H.Schonmann: Einstein relation for a class of interface models. Communications in Mathematical Physics 232 279 302 (2003). (72) T. Bodineau, R.H.Schonmann, S. Shlosman: 3D crystal: how flat its flat facets are? Communications in Mathematical Physics 255 747 766 (2005). (73) L. R. Fontes, R.H.Schonmann: Threshold θ 2 contact processes on homogeneous trees. Probability Theory and Related Fields 141 513 541 (2008). (74) L. R. Fontes, R.H.Schonmann: Bootstrap percolation on homogeneous trees has two phase transitions. Journal of Statistical Physics 132 839 861 (2008). (75) T. Mountford, R.H.Schonmann: The survival of the large dimensional threshold contactc processes. The Annals of Probability 37 1483-1501 (2009).

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