## Organizer(s) | Joel Lebowitz, Michael Kiessling | ## Archive | |

## Website | http://www.math.rutgers.edu/~lebowitz/Fall2014seminars.html |

## Upcoming Talks

## Thursday, February 5th |

## Haim Brezis, |

## "From the characterization of constant functions to isoperimetric inequalities" |

Time: 12:00 PM |

Location: Hill 705 |

Abstract: I will present a "common roof" to various, seemingly unrelated, known
statements asserting that integer-valued functions satisfying some kind
of mild regularity are constant. For this purpose I will introduce a new
function space B which is so large that it contains many classical
spaces, such as BV (=functions of bounded variation) , BMO
(=John-Nirenberg space of functions of bounded mean oscillation) and
some fractional Sobolev spaces. I will then define a fundamental closed
subspace B_0 of B contaning in particular W^{1,1}, VMO--- and thus
continuous functions---- H^{1/2} etc. A remarkable fact is that
integer-valued functions belonging to B_0 are necessarily constant. I
will also discuss connections of the B-norm to geometric concepts, such
as the perimeter of sets.
This is joint work with L. Ambrosio, J. Bourgain, A. Figalli and P. Mironescu. THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM! |

## Thursday, February 5th |

## Alessandro Giuliani , |

## "Height fluctuations in interacing dimers" |

Time: 2:00 PM |

Location: Hill 705 |

Abstract: Perfect matchings of Z^2 (also known as non-interacting dimers on the
square lattice) are an exactly solvable 2D statistical mechanics model.
It is known that the associated height function behaves at large
distances like a massless gaussian field, with the variance of height
gradients growing logarithmically with the distance. As soon as dimers
mutually interact, via e.g. a local energy function favoring the
alignment among neighboring dimers, the model is not solvable anymore
and the dimer-dimer correlation functions decay polynomially at infinity
with a non-universal (interaction-dependent) critical exponent. We prove
that, nevertheless, the height fluctuations remain gaussian even in the
presence of interactions, in the sense that all their moments converge
to the gaussian ones at large distances. The proof is based on a
combination of multiscale methods with the path-independence properties
of the height function.
Joint work with V. Mastropietro and F. Toninelli. |

## Thursday, February 12th |

## Roger Nussbaum, |

## "Perron-Frobenius Operators, Positive C^m Eigenvectors and the Computation of Hausdorff Dimension" |

Time: 12:00 PM |

Location: Hill 705 |

Abstract: We shall discuss a class of linear Perron-Frobenius operators L which,
under added assumptions, arise in the computation of Hausdorff dimension
for invariant sets of iterated function systems or graph directed
iterated function systems. We shall describe theorems which insure the
existence of a strictly positive, C^m eigenvector of L. In important
cases it is possible to obtain explicit bounds on second order (and
higher) partial derivatives of v. We shall indicate how (joint work
with Richard Falk) information about partial derivatives of v can be
used to obtain rigorous estimates of Hausdorff dimension (at least three
to four decimal point accuracy) for some previously intractable examples
like the set of complex continued fractions.
THERE WILL BE A BROWN BAG LUNCH BETWEEN 1-2PM! |

## Thursday, February 12th |

## Peter Nandori , |

## "Local thermal equilibrium for certain stochastic models of heat transport " |

Time: 2:00 PM |

Location: Hill 705 |

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. |