Where: MATh1313

Speaker: Mickey Salins (UMD) - http://www2.math.umd.edu/~msalins

Abstract: We study the limiting process of a stochastic partial differential equation driven by a fast Brownian motion. Interestingly, the limiting process involves a martingale whose quadratic variation is singular with respect to Lebesgue measure. Joint work with Zsolt Pajor-Gyulai.

Where: MATH3206

Speaker: David Nualart (University of Kansas) - http://www.math.ku.edu/~nualart/

Abstract:

We will present some new results on the one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter H in the space variable, assuming 1/4

Where: MATH1313

Speaker: Benjamin Kedem (UMD) - http://www.math.umd.edu/~bnk/

Abstract: In food safety and bio-surveillance in many cases it is desired

to estimate the probability that a contaminant such as some

insecticide or pesticide exceeds unsafe very high thresholds.

The probability or chance in question is then very small. To

estimate such a probability we need information about large values.

However, in many cases the data do not contain information about

exceedingly large contamination levels. A solution is suggested

whereby more information about small tail probabilities is

obtained by REPEATED FUSION of the real data with computer generated

"fake" data. The method provides short, yet reliable, interval

estimates from moderately large samples. An illustration is

provided using exposure data from the

National Health and Nutrition Examination Survey (NHANES).

Where: MATH1313

Speaker: Zsolt Pajor-Gyulai (UMD) - http://www2.math.umd.edu/~pgyzs/

Abstract: The diffusive limit of diffusion processes with periodic coefficients is well known to be a Brownian motion with an explicitly computable effective diffusion matrix. The topic of this talk is a situation when the coefficients are periodic only outside of an interface region of finite thickness. It turns out that the limit process is a semimartingale whose bounded variation part is proportional to the local time spent on the interface.

Where: MATH3206

Speaker: Yuri Lima (UMD) - http://www2.math.umd.edu/~yurilima/

Abstract: Given a finite connected graph, place a bin at each vertex. Two bins are called a pair if they share an edge of the graph. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. In this talk we discuss the limiting behavior of the proportion of balls in the bins. The results build on works of Benaim, Benjamini, Chen, Lima, and Lucas.

Where: MATH3206

Speaker: Renjie Feng (UMD) - http://www2.math.umd.edu/~renjie/

Abstract: In this talk, I will define random polynomials and their generalization to complex manifolds. The main result is regarding the landscape of such random holomorphic fields:

I will show that the expected value of the supremum of L^2 normalized random holomorphic fields of degree n on m-dimensional Kahler manifolds are asymptotically of order \sqrt{m\log n}. This is the joint work with S. Zelditch.

Where: MATH1313

Speaker: Mikko Stenlund (University of Helsinki) - http://www.math.helsinki.fi/mathphys/mikko.html

Abstract: Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. Recently, finer local limit theorems - yielding a Gaussian density multiplied by a highly oscillatory modulating factor - for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uniformly elliptic ballistic walks are now well understood. We complete the picture by proving a similar result for the only recurrent case, the balanced one, in which such a walk is diffusive. The method of proof is entirely different from the ballistic case.

See

http://front.math.ucdavis.edu/1206.5182

Where: Math3206

Speaker: Dmitry Dolgopyat (UMD) - http://www.math.umd.edu/~dolgop/

Abstract: We prove Local Limit Theorem for sums of independent random variables

satisfying appropriate tightness conditions. In particular we show that

the Local Limit Theorem holds if summands are uniformly bounded.

Where: MATH3206

Speaker: Janos Englander (University of Colorado Boulder) - http://euclid.colorado.edu/~englandj/MyBoulderPage.html

Abstract: We will discuss some spatial branching models where the particles interact with each other and some other models where the particles are put into a random environment, affecting the branching.

The main questions concern the large time behavior of these systems.

Where: MATH3206

Speaker: Amarjit Budhiraja (UNC, Chapel Hill) - http://www.unc.edu/~budhiraj/

Abstract: We present Moderate Deviation Principles for stochastic dynamical systems with small noise that is given in terms of Poisson random measures (PRM) and finite or infinite dimensional Brownian motions (BM). As applications we consider a family of stochastic partial differential equations with jumps and large collections of weakly interacting countable state Markov processes. Proofs rely on certain variational representations for expected values of nonnegative functionals of PRM and BM.

Where: MATH3206

Speaker: Peter Nandori (Courant) - http://www.cims.nyu.edu/~nandori/

Abstract: This talk is about nonequilibrium steady states (NESS) of a class of

stochastic models in which particles exchange energy with their 'local

environments' rather than directly with one another. The physical domain of the system can be a bounded region of R^d for any dimension d. We assume that the temperature at the boundary of the domain is prescribed and is nonconstant, so that the system is forced out of equilibrium. Our main result is local thermal equilibrium in the infinite volume limit. We also prove that the mean energy profile of NESS satisfies Laplace's equation for the prescribed boundary condition.

Our method of proof is duality: by reversing the sample paths of particle

movements, we convert the problem of studying local marginal energy

distributions at x to that of joint hitting distributions of certain random walks starting from x. This is a joint work with Yao Li and Lai-Sang Young.