The 2013 Southern California Probability Symposium will be held
on Saturday, December 7, 2013 on the **USC campus**.

All talks in Kaprelian Hall (KAP) 414.

9:15 | - | 9:50 | Refreshments | |

9:50 | - | 10:40 | Jason Schweinsberg (UCSD) | |

10:40 | - | 11:10 | Break | |

11:10 | - | 12:00 | Qi He (UCI) | |

12:00 | - | 2:00 | Lunch | |

2:00 | - | 2:50 | James Zhao (USC) | |

2:50 | - | 3:20 | Break | |

3:20 | - | 4:10 | Eviatar B. Procaccia (UCLA) | |

4:10 | - | 5:00 | Marco Frittelli (University of Milano, UCSB) | |

6:00 | - | Dinner |

Kaprelian Hall is on the western edge of campus, at the intersection of Vermont Ave. and 36th Place.

Free parking is available--just tell the parking booth attendant that you are going to the Probability Symposium (NOT Southern California Probability Symposium). Campus access is by either Entrance 5 (northern edge of campus at Jefferson Blvd. and McClintock Ave.) or Entrance 1 (off Exposition Blvd. on the south side of campus.) Either way, parking is in Parking Structure A, close to Kaprelian Hall where the conference takes place.

Please email Raya Feldman (feldman[at]pstat.ucsb.edu) if you would like to attend the dinner.

Thanks to Tom Liggett and Jim Pitman for putting together the following: The history of SCPS. 2011 2012

Individuals may add themselves to the email list. Please direct additions-- graduate students, former graduate students with new addresses, postdocs, and new faculty who would not have been on the list a year ago to the web page http://lists.imstat.org/mailman/listinfo/scpg.

This year's organizers are R. Feldman (feldman[at]pstat.ucsb.edu), J-P. Fouque (fouque[at]pstat.ucsb.edu), T. Ichiba (ichiba[at]pstat.ucsb.edu) and M. Ludkovski (ludkovski[at]pstat.ucsb.edu).

- 9:50 - 10:40 Jason Schweinsberg (UCSD)

**Title: ** Critical branching Brownian motion with absorption

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x > 0, particles move according to independent one-dimensional Brownian motions with the critical drift of negative the square root of 2, and particles are absorbed when they reach zero. Kesten (1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives ntil some large time t. These bounds improve upon results of Kesten (1978), and partially confirm nonrigorous predictions of Derrida and Simon (2007). We will also discuss results concerning the behavior of the process before the extinction time, as x tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle, and we obtain asymptotic results for the configuration of particles at a typical time. This is based on joint work with Julien Berestycki and Nathanael Berestycki.

- 11:10 - 12:00 Qi He (UCI)

**Title:** Large and moderate deviations of two-time-scale Markovian switching systems

In this talk, we consider large and moderate deviations for systems driven by continuous-time Markov chains with two-time scales and related optimal control prob- lems. In our setup we consider the inhomogeneous Markov chain rather than the homogeneous one which used in many literature before. The use of two-time-scale for- mulation stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory.

- 2:00 - 2:50 James Zhao (USC)

**Title:** Expand and Contract: A Technique for Combinatorial Sampling

Sampling uniformly from families of combinatorial objects is important for answering statistical questions about discrete data structures. While the difficulty of this problem depends on the complexity of the family, complicated families are often embedded inside simpler ones. In this talk, I will describe a sampling technique based on expanding the state space to a simpler family, then contracting back down to the original family while maintaining uniformity. I will show that this works well for a few simple examples, and also the more serious example of sampling graphs with given degrees, a difficult problem where this strategy substantially improves upon the best existing algorithms.

- 3:20 - 4:10 Eviatar B. Procaccia (UCLA)

**Title:** Quenched invariance principle for simple random walk on clusters in correlated percolation models.

Quenched invariance principle and heat kernel bounds for random walks on infinite percolation clusters and among i.i.d. random conductances in Z^d were proved during the last two decades.The proofs of these results strongly rely on the i.i.d structure of the models and some stochastic domination with respect to super-critical Bernoulli percolation. Many important models in probability theory and in statistical mechanics, in particular, models which come from real world phenomena, exhibit long range correlations. In this talk I will present a new quenched invariance principle, for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range correlations. This gives new results for random interlacements in dimension d>=3 at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness (which is believed to coincide with the whole supercritical regime). An essential ingredient of the proof is a new isoperimetric inequality for correlated percolation models. Joint work with Ron Rosenthal and Artem Sapozhnikov.

- 4:10 - 5:00 Marco Frittelli (University of Milano, UCSB)

**Title: ** Conditional evenly convex sets and the
representation of conditional maps

We introduce the concept of *conditional* evenly convex sets, as the generalization of the “static” notion of evenly convex set, and show that it is tailor made for the representation of conditional maps, as for example conditional quasi-convex risk measures.

In the classical approach, the conditional maps , are defined on vector spaces. Here instead we work in a random locally convex module. The intuition behind the use of modules is simple and natural: Consider an agent that is computing the risk of a time portfolio at an intermediate time . Thus the measurable random variables will act as scalars in the process of diversification of the portfolio, forcing to consider the set

as the domain of the conditional maps under consideration.

The use of the module approach and the notion of conditional evenly convex sets allow us to obtain a complete duality for quasi-convex monotone conditional maps. Joint paper with Marco Maggis. [Abstract file]