Wednesday, February 21, 2018 - 13:55 , Location: Skiles 005 , Paata Ivanisvili , Princeton University , firstname.lastname@example.org , Organizer: Galyna Livshyts
I will speak how to ``dualize'' certain martingale estimates related to the dyadic square function to obtain estimates on the Hamming and vice versa. As an application of this duality approach, I will illustrate how to dualize an estimate of Davis to improve a result of Naor--Schechtman on the real line. If time allows we will consider one more example where an improvement of Beckner's estimate will be given.
Series: Stochastics Seminar
Place Poi(m) particles at each site of a d-ary tree of height n. The particle at the root does a simple random walk. When it visits a site, it wakes up all the particles there, which start their own random walks, waking up more particles in turn. What is the cover time for this process, i.e., the time to visit every site? We show that when m is large, the cover time is O(n log(n)) with high probability, and when m is small, the cover time is at least exp(c sqrt(n)) with high probability. Both bounds are sharp by previous results of Jonathan Hermon's. This is the first result proving that the cover time is polynomial or proving that it's nonpolymial, for any value of m. Joint work with Christopher Hoffman and Matthew Junge.
Wednesday, February 14, 2018 - 13:55 , Location: Skiles 005 , Dmitry Ryabogin , Kent State University , email@example.com , Organizer: Galyna Livshyts