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  Dmitry Ioffe    (April 5th, 1963, Moscow, Russia - October 1st 2020, Haifa, Israel) was an Israeli mathematician, working in statistical mechanics. He was a leading expert in probabilistic aspects of the theory and made basic contributions to solutions of a number of fundamental problems.

 Biography  edit

Dima Ioffe was born in Moscow. In 1976 his family applied for permission to leave the USSR for Israel but was refused. In 1985 he graduated (got an analog of MA) from Moscow State Mining University and early in 1987 was able to leave for Israel with his wife and 2-year-old daughter. In 1991 he got a PhD in mathematics from Technion, Israel with his thesis supervised by Ross Pinsky. Dima started to work in statistical mechanics during his two postdoc years, the first at the University of California, Davis and the second at the Courant Institute. After that, he worked for two years as an assistant professor in the Northwestern University and then two years in the Weierstrass Institute of Analysis and Stochastics (WIAS) in Berlin before getting back to the Technion in 1997. He had 6 PhD students and 16 postdocs, Th. Bodineau, P. Caputo, N. Crawford, O. Louidor and Y. Velenik among the latter. Dima was aware of his terminal illness since the summer of 2017, but continued his research with the same vigor and strength. He died at the age of 57 at the very peak of his scientific activity.

 Awards  edit


 * 1991 — Technion, E. Landau prize for a distinguished D. Sc. thesis.
 * 2000 — Kurt Mahler prize in mathematics.
 * 2006 — Prix de l’Institut Henri Poincare 2004/05.
 * 2011 — Humboldt Research Award.
 * 2006 — Prix de l’Institut Henri Poincare 2004/05.
 * 2011 — Humboldt Research Award.
 * 2011 — Humboldt Research Award.

 Professional achievements  edit

Hard problems in statistical mechanics are typically associated with behavior of systems near critical temperatures. Ioffe’s early work which immediately established him as a leader in the field [1], [2], [3] was a far reaching extension of a celebrated 1992 result of Dobrushin- Kotecky- Shlosman concerning phase boundaries of two dimensional Ising ferromagnet (the Wulff problem) from low to all subcritical temperatures.

At the end of the 90s an alternative analytic approach to the construction of Wulff crystals was developed by Bodineau, Pisztora, Cerf that substantially differed from the DKS theory (see [4] for a detailed review of this area of research). In [5] the approach was adapted to properly take into account the boundary conditions, which in particular allowed to study the associated wetting transition and to provide a microscopic justification of the Winterbottom construction of the equilibrium crystal shape in the presence of a substrate.

In a series of papers [6],[7],[8], partly joint with M. Campanino and Y. Velenik, Ioffe developed a mathematically rigorous Ornstein-Zernike theory for a variety of models, including self avoiding walk, Bernoulli percolation and Ising ferromagnet, at all temperatures above criticality and in any dimension. In particular, it contained the first non-perturbative proof that did not rely on integrability. It was a part of a long program by Dima and collaborators spanning roughly the last two decades of Dima’s life. In the framework of this program it became possible to justify and discover a number of important applications of the OZ-theory (see e.g. [9],[11],[19] and references therein).

Further main Dima’s contributions include, among others, the first use of re- generation techniques for stretched self-interactive polymers [10] (see also [12] for a survey of his results concerning polymers in random environment), the introduction of space-time random current representations [13], and subsequent developments for quantum lattice systems, metastability and large deviations [14], [15]. His probabilistic intuition and extensive technical skills led him to the invention of ”Diamond” representation for interfaces of 2D systems which made it possible to treat them as random walks. Along with the mentioned contribution to the Ornstein-Zernike theory, this allowed to treat a variety of challenging problems related to random walks and interfaces [16], [17] (see also [18] for the culmination of this line of research). In the three last published papers (written, along with [18], [19] and three more papers to be published, already after his illness was discovered) he studied large scale behavior of non-intersecting Brownian bridges above a hard wall [20],[21] and certain problems associated with stochastic representation of quantum spin systems [22].

 Selected Publications  edit

1. D. Ioffe (1994), Large deviations for the 2D Ising model: a lower bound without cluster expansions, J. Statistical Physics 74, 411-432.

2. D. Ioffe (1995) Exact large deviation bounds up to Tc for the Ising model in two dimensions, Probability Th. Related Fields, 102, 313-330.

3. D. Ioffe and R.H. Schonmann (1998), Dobrushin-Kotecky-Shlosman theorem up to the critical temperature, Comm. Math. Physics 199, 117-167.

4. T. Bodineau, D. Ioffe and Y. Velenik, (2000) Rigorous probabilistic analysis of equilibrium crystal shapes. Probabilistic techniques in equilibrium and non- equilibrium statistical physics, J. Math. Physics 30, 1033-1098.

5. T. Bodineau, D. Ioffe and Y. Velenik, (2001) Winterbottom construction for finite range ferromagnetic models: an L1-approach, J. Stat. Physics 105, 93-131.

6. D. Ioffe, (1998) Ornstein-Zernike behavior and analyticity of shapes for self- avoiding walk on Zd, Markov Processes Related Fields 4, 323-350.

7. M. Campanino and D. Ioffe (2002), Ornstein-Zernike theory for the Bernoulli bond percolation on Z d, Annals of Probability 30, 652-682.

8. M. Campanino, D. Ioffe and Y. Velenik (2003), Ornstein-Zernike theory for finite range Ising models above Tc, Probability Th. Related Fields 125, 305-349.

9. M. Campanino, D. Ioffe and O. Louidor (2010) Finite Connections for Supercritical Bernoulli Bond Percolation in 2D, Markov Processes Related Fields 16, 225266.

10. D. Ioffe and Y. Velenik (2012), Crossing random walks and stretched polymers at weal disorder, Annals of Probability 40, 714-742.

11. D. Ioffe and Y. Velenik (2012), Self-attractive random walks: the case of critical drifts, Comm. Math. Physics 313, 209235.

12. D. Ioffe (2015), Multidimensional random polymers: a renewal approach, in ”Probability in Complex Physical Systems, in honor of E. Bolthausen”, J. Gartner et al (eds), Springer Proceedings in Math. 11, 339-369.

13. N. Crawford and D. Ioffe (2010), Random current representation for transverse field Ising models, Comm. Math. Physics 296, 225-266.

14. D. Ioffe (2009), Stochastic geometry of classical and quantum Ising models, in ”Methods of Contemporary Statistical Physics”, R. Kotecky ed., LNM Springer 2144, pp 87-127.

15. A. Bianchi, A. Bovier and D. Ioffe (2012), Pointwise estimates in exponential laws in metastable systems via coupling methods, Annals of Probability 40, 339-371.

16. D. Ioffe, S. Shlosman and Y. Velenik (2015), An Invariance Principle to Ferrari-Spohn Diffusions Comm. Math. Physics 336, 905-932.

17. D. Ioffe, Y. Velenik and V. Wachtel (2018), Dyson Ferrari-Spohn diffusions and ordered walks under area tilts, Probability Th. Related Fields 170, 11-47.

18. D. Ioffe, S. Ott, S. Shlosman and Y. Velenik (2020), Critical prewetting in the 2d Ising model,

19. D. Ioffe, S. Ott, Y. Velenik and V. Wachtel (2020), Invariance Principle for a Potts Interface Along a Wall, J. Stat. Physics 180, 832-861.

20. P. Caputo, D. Ioffe and V. Wachtel (2019), Tightness and Line Ensembles for Brownian Polymers Under Geometric Area Tilts, Statistical Mechanics of Classical and Disordered Systems, Springer Proceedings in Mathematics & Statistics 293, 241–266.

21. P. Caputo, D. Ioffe and V. Wachtel (2019), Confinement of Brownian polymers under geometric area tilts, Electron. J. Probability 24, 121.

22. D. Ioffe and B. Toth (2020), Split and Merge in Stationary Random Stirring on Lattice Torus, J. Stat. Physics 180, 630-653.

 See also  edit

https://web.iem.technion.ac.il/site/dmitry-dima-ioffe-1963-2020/ https://www.researchgate.net/scientific-contributions/Dmitry-Ioffe-9345970 https://www.hcm.uni-bonn.de/en/hcm-news/obituary-to-dmitry-ioffe/ https://www.minerva.mpg.de/62875/in-remembrance-of-dmitry-ioffe

 References  edit