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Professor Dmitry Ioffe

General Information
Dima  Ioffe received a  M.Sc. in  System Engineering  from Moscow Mining Institute. Shortly after his repatriation to Israel in 1987, he joined the graduate program at the Department of Mathematics at the Technion from which he received a D.Sc. degree in Mathematics. Following his graduation in 1991, he held visiting positions at UC Davis (1991-92), Courant Institute at the NYU (1992-93) and Northwestern University (1993-95). In 1995, he joined the group "Interacting Random Systems" at the Weierstrass Institute of Applied Mathematics and Stochastics in Berlin. He returned to Israel in 1997 to assume a position at the Faculty of Industrial Engineering and Management at the Technion.

Research Summary
Dima Ioffe has been doing research in various branches of the Probability Theory focused on the development and application of probabilistic methods to the problems of Science and Engineering. His main contributions over the past several years have been in the area of lattice random fields-an interdisciplinary subject which draws inspiration and problems from the fields of Statistical Mechanics, Image Processing, Pattern Recognition, and others. More specifically, recent works of  Ioffe address both static and dynamic aspects of phase transitions; a complex phenomenon which manifests itself in the breakdown of  spatial homogeneity and in  creation of long-range dependence between the observables. A typical problem then is to explain and deduce a formation of relatively simple macroscopic deterministic patterns which, in an appropriate scaling limit, would approximate huge microscopic systems with such complex interactions. An effective rigorous treatment of these problems goes well beyond conventional methods of the classical Probability Theory and requires an introduction of new ideas and techniques.

Current Research Projects
  • Stochastic geometry of classical and quantum spin systems.
  • Random interfaces, random fields and interacting particle systems.
  • Metastability and phase segregation.
  • Percolation. Polymers in random environment.

Selected Publications

  • Ioffe, D., Shlosman. S. and Velenik, Y. (2014), An invariance principle to Ferrari-Spohn diffusions, preprint.
  • Coquille, L., Duminil-Copin, H., Ioffe, D. and Velenik, Y. (2014), On the Gibbs state of the   noncritical Potts model on Z2Prob. Theor. Rel. Fields. 158, 1-2, 477--512.
  • Ioffe, D. and Levit, A. (2013), Ground states for mean field models with a transverse component, J.Stat.Phys. 151, 6, 1140--1161.
  • Ioffe, D. and Velenik, Y. (2013),  An almost sure CLT for stretched polymers,   EJP. 18,  97, 1--20.
  • Friedli, S. Ioffe, D. and Velenik, Y. (2013), Subcritical percolation with a line of defects,  Ann.Prob. 41, 3B, 2013--2046. 
  • Ioffe, D. and Velenik, Y. (2012), Self-attracting random walks: The case of critical drifts, Comm. Math.  Phys.. 313, 209--235.  
  • Ioffe, D. and Velenik, Y. (2012), Stretched polymers in random environment, in Probability in Complex Physical Systems, in honour of E. Bolthausen and J. Gartner, J.-D. Deuschel et al. (eds), Springer Proceedings in Mathematics 11, 339--369.
  • Ioffe, D. and Velenik, Y. (2012), Crossing random walks and stretched polymers at weak disorder, Ann.Prob. 40, 2, 714--742.
  • Bianchi, A., Bovier, A. and Ioffe, D. (2012), Pointwise estimates and exponential laws in metastable systems via coupling methods, Ann.Prob. 40, 1, 339--371.
  • Ioffe, D. and Velenik, Y. (2010), The statistical mechanics of stretched polymers, Braz. J. Probab. Stat. 24, 2, 279--299.
  • Campanino, M., Ioffe, D. and Louidor, O. (2010), Finite connections for supercritical Bernoulli bond percolation in 2D , Mark. Proc. Rel. Fields 16, 225--266.
  • Crawford, N. and Ioffe, D. (2010), Random Current Representation for Transverse Field Ising Model , Comm. Math. Phys. 296, 2, 447--474.
  • Bianchi, A., Bovier, A. and Ioffe, D. (2009), Sharp Asymptotics for Metastability in the Random Field Curie-Weiss Model , EJP 14, 1541--1603.
  • Ioffe, D. (2009), Stochastic Geometry of Classical and Quantum Ising Models , in Methods of Contemporary Mathematical Statistical Physics, R. Kotecky editor, LNM 1970, 87--126, Springer.
  • Chayes, L., Crawford, N., Ioffe, D. and Levit, A. (2008), The Phase Diagram of the Quantum Curie-Weiss Model, J.Stat. Phys. 133, 1, 131--149..
  • Ioffe, D. and Velenik, Y. (2008), Ballistic Phase of Self-Interacting Random Walks, Analysis and Stochastics of Growth Processess and Interface Models, 55-79, Morters, P., Moser, R., Penrose, M., Schwetlick, H. and Zimmer, J. editors, Oxford University Press.
  • Ioffe, D. and Shlosman, S. (2008), Ising model fog drip: the first two droplets, In and Out of Equilibrium 2, Progress in Probability 60, 365--382, Birkhauser.
  • Campanino, M., Ioffe, D. and Velenik, Y. (2008), Fluctuation theory of connectivities for subcritical random cluster models, Ann.Prob. 36, 4, 1287--1321.
  • Ioffe, D., Levit, A. (2007), Long range order and giant components of quantum random graphs, Mark. Proc. Rel. Fields 13, 3, 469--492.
  • Ioffe, D., Velenik, Y. and Zahradnik, M. (2006), Entropy-driven phase transition in a polydisperse hard-rods lattice system, J. Stat. Phys. 122, 4, 761--786.
  • Greenberg, L. and Ioffe, D. (2005), On an invariance principle for phase separation lines, Ann. Inst. H. Poinc. Probab. Statist. 45, 871--885.
  • Bodineau, Th. and Ioffe, D. (2004), Stability of interfaces and stochastic dynamics in the regime of partial wetting, Ann. Inst. H. Poinc. Theor. Physics, 5, 871--914.
  • Campanino, M., Ioffe, D. and Velenik, Y. (2004), Random path representation and sharp correlations asymptotics at high-temperatures, Stochastic analysis of large scale interacting systems, Adv. Stud. Pure Math., 39, 29--52, Math. Soc. Japan, Tokyo.
  • Caputo, P. and Ioffe, D. (2003), Finite volume approximation of the effective diffusion matrix: the case of independent bond disorder, Ann. Inst. H. Poinc. Probab. Statist.39, 3, 505--525
  • Campanino, M., Ioffe, D. and Velenik, Y. (2003), Ornstein-Zernike theory for finite range Ising models above Tc, Prob. Theor. Rel. Fields 125, 305--349.
  • Campanino, M. and Ioffe, D. (2002) , Ornstein-Zernike theory the Bernoulli bond percolation on Zd, Annals Prob. 30, 2, 652--682.
  • Ioffe, D., Shlosman, S. and Velenik, Y. (2002), 2D models of statistical physics with continuous symmetry: the case of singular interactions, Comm.Math.Phys. 226, 433--454.
  • Ioffe, D. (2002), A note on the quantum version of the Widom-Rowlinson model, J.Stat.Phys. 106, 1-2, 375--384.
  • Bodineau, Th., Ioffe, D. and Velenik, Y. (2001), Winterbottom construction for finite range ferromagnetic models: an L1-approach, J.Stat.Phys., 105, 1-2, 93-131.
  • Bodineau, Th., Ioffe, D. and Velenik, Y. (2000), Rigorous probabilistic analysis of equilibrium crystal shapes, J.Math.Phys., 41, 1033--1098.
  • Deuschel, J-D., Giacomin, G. and Ioffe, D. (2000), Large deviation and concentration properties for a class of nabla phi interface models, Prob.Theor.Rel.Fields. 117, 1, 49--111 .
  • Ioffe, D. and Velenik, Y. (2000), A Note on the Decay of Correlations Under δ-Pinning, Prob.Theor.Rel.Fields. 116, 379--389.
  • Ioffe, D. (1998), Ornstein-Zernike behaviour and analyticity of shapes for self-avoiding walks on Zd, Mark. Proc. Rel. Fields, 4, 323--350.
  • Ioffe, D. and Schonmann, R. (1998), Dobrushin-Kotechy-Shlosman theorem up to the critical temperature , Comm. Math. Phys.199, 117--167.
  • Bolthausen, E. and Ioffe, D. (1997), Harmonic crystal on the wall: A microscopic approach, Comm. Math. Phys. 187 (3), 523--566.
  • Ioffe, D. (1996), Extremality of the disordered state for the Ising model on general trees, Progress in Probability40, editors B.Chauvin, S.Cohen and A.Rouault, Birkh"{a}user, 3--14.
  • Ioffe, D. (1996), On the extremality of the disordered state for the Ising model on the Bethe lattice. Lett. Math. Phys. 37 (2), 137--143.
  • Ioffe, D. (1995), Exact large deviation bounds up to Tc for the Ising model in two dimensions, Probability Theory and Related Fields 102, 313--330.
  • Ioffe, D. (1994), Large deviations for the 2D Ising model: a lower bound without cluster expansions, J.Stat.Phys., 74, 411--432.
  • Ioffe, D. and Pinsky, R.G. (1994), Positive harmonic functions vanishing on the boundary for the Laplacian in unbounded horn-shaped domains, Trans.Amer.Math.Soc. 342, 773--791.
  • Ioffe, D. (1991), On some applicable versions of abstract large deviation theorems, Ann.Prob., 19, 1629--1639.

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