We introduce another three of this year’s Medallion Lecturers: Jean Bertoin, Davar Khoshnevisan and Ming Yuan. Jean will be giving his Medallion Lecture at the IMS Annual Meeting in Vilnius, Lithuania, July 2–6, 2018; Davar will be speaking at the Stochastic Processes and Their Applications (SPA 2018) meeting in Gothenburg, Sweden (June 11–15); Ming’s lecture will be at JSM in Vancouver, July 28–August 2, 2018. More special lecture previews in the next issue…
Medallion preview: Jean Bertoin
Jean Bertoin studied at the Ecole Normale Supérieure de Saint Cloud, France, and received his PhD from University Pierre-et-Marie Curie (Paris VI) in 1987 under the supervision of Marc Yor. He is currently a Professor at the University of Zürich, having held positions at the University Pierre-et-Marie Curie, at the CNRS, and at Ecole Normale Supérieure (ENS) in Paris. His research interests include notably Lévy processes, random trees, branching processes, fragmentation and coalescence dynamics. He was awarded the CNRS bronze medal (1993), the Rollo Davidson prize (1996) and the Thérèse Gautier prize (2015); he is also a corresponding member of the Academia Mexicana de Ciencias.
Jean will be giving his Medallion Lecture at the IMS Annual Meeting in Vilnius, Lithuania, July 2–6, 2018
Pure fragmentation processes were introduced by A.N. Kolmogorov in 1941, as models for an inert mass which undergoes repeatedly random dislocations. To deal with dynamics which are mathematically tractable, one assumes the branching property, that is, that different fragments evolve independently. Further, one often focuses on a self-similar setting, in the sense that the statistics of the process starting at time 0 from a single mass m>0 can be reduced up to a simple scaling transformation to that for a unit mass m=1. The distribution of a pure fragmentation process is then determined by the index of self-similarity, a so-called dislocation measure that encodes the statistics of the sudden dislocations, and an erosion coefficient that accounts for the possible continuous decay of the masses of the fragments.
Growth-fragmentation processes can be thought of as fragmentation processes to which a growth phenomenon has been incorporated. They have been introduced in Life Science as models of populations of cells or bacteria, which evolve by growth and division. They have also appeared more recently in the framework of random planar geometry.
The incorporation of growth changes fundamentally the dynamics of fragmentation processes. For instance, growth may “compensate” dislocations and avoid instantaneous shattering despite of an extremely high intensity of dislocations. On the other hand, growth may also induce “local” explosions, in the sense that an infinity of macroscopic particles may be present at the same time. Typically, this may occur when intense and repeated dislocations produce a huge number of extremely small particles, and still the growth rate for small particles is sufficiently strong to enable some of them to reach a macroscopic size in a finite time.
In this lecture, I will describe the general construction of (self-similar) growth-fragmentation processes in terms of a cell system, whose evolution is related to that of a Lévy process without positive jumps. In particular, negative jumps of the latter are interpreted as birth events for the cell system, in the sense that at each time a cell makes a negative jump with size −y, a new particle with size y is created and starts evolving independently of her mother. I will also discuss the connection with branching random walks, and some remarkable Malthusian martingales that arise in this framework. In particular, this leads to an important area measure, which plays a central role in a variety of limit theorems.
Medallion preview: Davar Khoshnevisan
Davar Khoshnevisan received his PhD in 1989 from the Department of Statistics at the University of California at Berkeley under the supervision of Professor P.W. Millar. Davar was a postdoc at MIT and the University of Washington before he joined the faculty of Mathematics at the University of Utah in 1993, where he is now Professor and Chair of the Department of Mathematics. Davar works in stochastic analysis, especially on qualitative and quantitative analysis of stochastic partial differential equations. He is a Fellow of the IMS, an Oberwolfach–Simons Visiting Professor (2014), principal lecturer at the CBMS Conference on Stochastic Partial Differential Equations in Lansing, MI (2013), plenary speaker at the 34th Conference on Stochastic Processes and Their Applications (SPA) in Osaka (2010), and an awardee of the Rollo Davidson Prize (1998).
Davar Khoshnevisan’s Medallion Lecture will be given at SPA 2018 in Gothenburg, Sweden, in June 2018.
Analysis of a Stratied Kraichnan Model
We study quantitative, as well as qualitative, aspects of the problem of turbulent transport of a passive scalar quantity (such as the temperature, or concentration, of an injected dye) in a naturally arising, random, stratied, 2-dimensional, incompressible velocity field.
Among other things, we introduce a rigorous framework for describing the multifractal structure of the dissipation times of the passive quantity of interest. Some of these multi-fractal properties have been predicted earlier in the physics and engineering literatures. All of the unexplained terms of the abstract will be described more precisely in the talk.
This is based on joint work with Jingyu Huang.
Medallion preview: Ming Yuan
Ming Yuan is Professor of Statistics at Columbia University. He was previously Senior Investigator at Morgridge Institute for Research and Professor at University of Wisconsin at Madison, and prior to that, Coca-Cola Junior Professor at Georgia Institute of Technology. His research interests lie broadly in statistics and its interface with other quantitative and computational fields such as optimization, machine learning and computational biology. In particular, his recent research focuses on algorithmic and theoretical aspects of high dimensional data analysis and its applications. He serves or has served on the editorial boards of The Annals of Statistics, Bernoulli, Electronic Journal of Statistics, Journal of the American Statistical Association, Journal of the Royal Statistical Society Series B, and Statistical Science. He is a recipient of the John van Ryzin Award (2004; ENAR), a CAREER Award (2009; NSF), the Guy Medal in Bronze (RSS; 2014), and a Leo Breiman Junior Researcher Award (ASA Section on SLDM; 2017).
Ming’s Medallion Lecture will be given at the Joint Statistical Meetings (JSM) in Vancouver, July 28–August 2, 2018.
Statistical Analysis of Large Tensors
Large amount of multidimensional data in the form of multilinear arrays, or tensors, arise routinely in modern applications from such diverse fields as chemometrics, genomics, physics, psychology, and signal processing among many others. At the present time, our ability to generate and acquire them has far outpaced our ability to effectively extract useful information from them. There is a clear demand to develop novel statistical methods, efficient computational algorithms, and fundamental mathematical theory to analyze and exploit information in these types of data. Such an endeavor, however, faces unique challenges from both conceptual and computational points of view.
In spite of the challenges, we are at a vantage point to address some of the most pressing and core issues in the statistical analysis of these types of data thanks to recent advances in high dimensional statistics, high dimensional probability, and large scale nonlinear optimization. In this lecture, I will illustrate how we can build upon these advances and develop statistical methods, algorithms and theory to efficiently, both statistically and computationally, analyze large scale data in the form of tensors.