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−  == Thursday, January 26, Timo Seppäläinen, University of Wisconsin  Madison ==  +  == Thursday, September 27, Scott McKinley, University of Florida == 
   
−  Title: The exactly solvable loggamma polymer  +  Title: TBA 
   
−  Abstract: Among 1+1 dimensional directed lattice polymers, loggamma distributed weights are a special case that is amenable to various useful exact calculations (an ''exactly solvable'' case). This talk discusses various aspects of the loggamma model, in particular an approach to analyzing the model through a geometric or "tropical" version of the RobinsonSchenstedKnuth correspondence.  +  Abstract: TBA 
−   
−  == Thursday, February 9, Arnab Sen, Cambridge ==
 
−   
−  Title: Random Toeplitz matrices
 
−   
−  Abstract: Random Toeplitz matrices belong to the exciting area that lies at the intersection of the usual Wigner random matrices and random Schrodinger operators. In this talk I will describe two recent results on random Toeplitz matrices. First, the maximum eigenvalue, suitably normalized, converges to the 24 operator norm of the wellknown Sine kernel. Second, the limiting eigenvalue distribution is absolutely continuous, which partially settles a conjecture made by Bryc, Dembo and Jiang (2006). I will also present several open questions and conjectures.
 
−   
−  This is a joint work with Balint Virag (Toronto).
 
−   
−   
−  == Thursday, February 16, Benedek Valko, University of Wisconsin  Madison ==
 
−   
−  Title: Point processes and carousels
 
−   
−  Abstract: For several classical matrix models the joint density of the eigenvalues can be written as an expression involving a Vandermonde determinant raised to the power of 1, 2 or 4. Most of these examples have betageneralizations where this exponent is replaced by a parameter beta>0.
 
−  In recent years the point process limits of various beta ensembles have been derived. The limiting processes are usually described as the spectrum of certain stochastic operators or with the help of a coupled system of SDEs.
 
−  In the bulk beta Hermite case (which is the generalization of GUE) there is a nice geometric construction of the point process involving a Brownian motion in the hyperbolic plane, this is the Brownian carousel. Surprisingly, there are a number of other limit processes that have carousel like representation. We will discuss a couple of examples and some applications of these new representations.
 
−   
−  Joint with Balint Virag.
 
−   
−   
−  == Thursday, February 23, Tom Kurtz, University of Wisconsin  Madison ==
 
−   
−  Title: Particle representations for SPDEs and strict positivity of solutions
 
−   
−  Abstract: Stochastic partial differential equations arise naturally as limits of finite systems of interacting particles. For a variety of purposes, it is useful to keep the particles in the limit obtaining an infinite exchangeable system of stochastic differential equations. The corresponding de Finetti measure then gives the solution of the SPDE. These representations frequently simplify existence, uniqueness and convergence results. The support properties of the measurevalued solution can be studied using Girsanov change of measure techniques. The ideas will be illustrated by a model of asset prices set by an infinite system of competing traders. These latter results are joint work with Dan Crisan and Yoonjung Lee.
 
−   
−   
−  == Wednesday, February 29, 2:30pm, Scott Armstrong, University of Wisconsin  Madison ==
 
−   
−  VV B309
 
−   
−  Title: PDE methods for diffusions in random environments
 
−   
−  Abstract: I will summarize some recent work with Souganidis on the stochastic
 
−  homogenization of (viscous) HamiltonJacobi equations. The
 
−  homogenization of (special cases of) these equations can be shown to
 
−  be equivalent to some wellknown results of Sznitman in the 90s on the
 
−  quenched large deviations of Brownian motion in the presence of
 
−  Poissonian obstacles. I will explain the PDE point of view and
 
−  speculate on some further connections that can be made with
 
−  probability.
 
−   
−  == Wednesday, March 7, 2:30pm, Paul Bourgade, Harvard ==
 
−   
−  VV B309
 
−   
−  Title: Universality for beta ensembles.
 
−   
−  Abstract: Wigner stated the general hypothesis that the distribution of eigenvalue spacings of large complicated quantum systems is universal in the sense that it depends only on the symmetry class of the physical system but not on other detailed structures. The simplest case for this hypothesis is for ensembles of large but finite dimensional matrices. Spectacular progress was done in the past two decades to prove universality of random matrices presenting an orthogonal, unitary or symplectic invariance. These models correspond to loggases with respective inverse temperature 1, 2 or 4. I will report on a joint work with L. Erdos and H.T. Yau, which yields local universality for the loggases at arbitrary temperature, for analytic external potential. The involved techniques include a multiscale analysis and a local logarithmic Sobolev inequality.
 
−   
−  == Thursday, March 8, William Stanton, UC Boulder ==
 
−   
−  Title: An Improved RightTail Upper Bound for a KPZ "Crossover Distribution"
 
−   
−  Abstract: In the last decade, there has been an explosion of research on KPZ universality: the notion that the KardarParisiZhang stochastic PDE from statistical physics describes the fluctuations of a large class of models. In 2010, Amir, Corwin, and Quastel proved that the KPZ equation arises as a scaling limit of the Weakly Asymmetric Simple Exclusion Process (WASEP). In this sense, the KPZ equation interpolates between the KPZ universality class and the EdwardsWilkinson class. Thus, the distributions of height functions of the KPZ equation are called the "crossover distributions." In this talk, I will introduce the notion of KPZ universality and the crossover distributions and present a new result giving an improved upper bound for the righttail of a particular crossover distribution.
 
−   
−  == Friday, April 13, 2:30pm, Gregory Shinault, UC Davis ==
 
−  VV B305
 
−   
−  Title: Inhomogeneous Tilings of the Aztec Diamond
 
−   
−  Random domino tilings of the Aztec diamond have been a
 
−  subject of much interest in the past 20 years. The main result of the
 
−  subject, the Arctic Circle theorem, is a gem of modern mathematics
 
−  which gives the limiting shape of the tiling. When we examine
 
−  fluctuations around the limiting shape, we do not see a Gaussian
 
−  distribution as one might expect in classical probability. Instead we
 
−  see the TracyWidom GUE distribution of random matrix theory. These
 
−  theorems were originally proven for a random tiling chosen by a
 
−  uniform distribution. In this talk we examine the effects of choosing
 
−  the tiling via a distribution in an inhomogeneous environment (and
 
−  we'll explain what we mean by this!).
 
−   
−  == Thursday, April 19, Nancy Garcia, Universidade Estadual de Campinas ==
 
−  Title: Perfect simulation for chains and processes with infinite range
 
−   
−  Abstract: In this talk we discuss how to perform Kalikowtype decompositions
 
−  for discontinuous chains of infinite memory and for interacting particle
 
−  systems
 
−  with interactions of infinite range. Then, we will show how this
 
−  decomposition can be used
 
−  to generate samples from these systems.
 
−   
−  == Thursday, April 26, Jim Kuelbs, University of Wisconsin  Madison ==
 
−   
−   
−  A CLT for Empirical Processes and Empirical Quantile Processes Involving Time Dependent Data
 
−   
−  We establish empirical quantile process CLT's based on <math>n</math> independent copies of a stochastic process <math>\{X_t: t \in E\}</math> that are uniform in <math>t \in E</math> and quantile levels <math>\alpha \in I</math>, where <math>I</math> is a closed subinterval of <math>(0,1)</math>. Typically <math>E=[0,T]</math>, or a finite product of such intervals. Also included are CLT's for the empirical process based on <math>\{I_{X_t \le y}  \rm {Pr}(X_t \le y): t \in E, y \in R \}</math> that are uniform in <math>t \in E, y \in R</math>. The process <math>\{X_t: t \in E\}</math> may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent increment stable processes, and martingales.
 
−   
−  == Monday, April 30, 2:30pm, Lukas Szpruch, Oxford ==
 
−  VV B337
 
−   
−  Title: Antithetic multilevel Monte Carlo method.
 
− 
 
−   
−  We introduce a new multilevel Monte Carlo
 
−  (MLMC) estimator for multidimensional SDEs driven by Brownian motion.
 
−  Giles has previously shown that if we combine a numerical approximation
 
−  with strong order of convergence $O(\D t)$ with MLMC we can reduce
 
−  the computational complexity to estimate expected values of
 
−  functionals of SDE solutions with a rootmeansquare error of $\eps$
 
−  from $O(\eps^{3})$ to $O(\eps^{2})$. However, in general, to obtain
 
−  a rate of strong convergence higher than $O(\D t^{1/2})$ requires
 
−  simulation, or approximation, of \Levy areas. Through
 
−  the construction of a suitable antithetic multilevel correction estimator,
 
−  we are able to avoid the simulation of \Levy areas and still achieve an
 
−  $O(\D t2)$ variance for smooth payoffs, and almost an $O(\D t^{3/2})$ variance for
 
−  piecewise smooth payoffs,
 
−  even though there is only $O(\D t^{1/2})$ strong convergence. This
 
−  results in an $O(\eps^{2})$ complexity for estimating the
 
−  value of European and Asian put and call options.
 
−  We also comment on the extension of the antithetic
 
−  approach to pricing Asian and barrier options.
 
−   
−  == Wednesday, May 2, 2:30pm, Wenbo Li, University of Delaware ==
 
−   
−  VV B337
 
−   
−  Title: Probabilities of all real zeros for random polynomials
 
−   
−  Abstract: There is a long history on the study of zeros of random polynomials whose coefficients are independent, identically distributed, nondegenerate random variables.
 
−  We will first provide an overview on zeros of random functions and then show exact and/or asymptotic bounds on probabilities that all zeros of a random polynomial are real under various distributions.
 
−  The talk is accessible to undergraduate and graduate students in any areas of mathematics.
 
−   
−  == Thursday, May 3, Samuel Isaacson, Boston University ==
 
−   
−  Title: Relationships between several particlebased stochastic reactiondiffusion models.
 
−   
−  Abstract:
 
−  Particlebased stochastic reactiondiffusion models have recently been used to study a number of problems in cell biology. These methods are of interest when both noise in the chemical reaction process and the explicit motion of molecules are important. Several different mathematical models have been used, some spatiallycontinuous and others latticebased. In the former molecules usually move by Brownian Motion, and may react when approaching each other. For the latter molecules undergo continuous time randomwalks, and usually react with fixed probabilities per unit time when located at the same lattice site.
 
−   
−  As motivation, we will begin with a brief discussion of the types of biological problems we are studying and how we have used stochastic reactiondiffusion models to gain insight into these systems. We will then introduce several of the stochastic reactiondiffusion models, including the spatially continuous Smoluchowski diffusion limited reaction model and the latticebased reactiondiffusion master equation. Our work studying the rigorous relationships between these models will be presented. Time permitting, we may also discuss some of our efforts to develop improved numerical methods for solving several of the models.
 