[ABE-L] A sample-path large deviation principle for dynamic Erdos-Renyi random graphs

Seg Jul 11 22:21:15 -03 2022

Our next Asia-Pacific Seminar in Probability and Statistics will take place on
Wednesday, 13 July at 5:30pm  NZ

Speaker: Peter Braunsteins, KAUST

Title: A sample-path large deviation principle for dynamic Erdos-Renyi random graphs

Abstract: In this talk, we consider dynamic Erdős-Rényi random graphs on $n$ vertices in which each edge switches on at rate $\lambda$ and switches off at rate $\mu$, independently of other edges. We work in the space of \emph{graphons}, where our focus is on the evolution of the associated empirical graphon in the limit as $n \to \infty$. Our main result is a large deviation principle (LDP) for the sample path of the empirical graphon observed until a fixed time horizon. The rate of the LDP is $n(n-1)/2$ and the rate function is a specific action integral on the space of graphon trajectories. We apply the LDP to identify (i) the most likely path from a typical outcome of an Erdős-Rényi random graph at time 0 to a graph with an atypically large density of $d$-regular subgraphs at time $T$, and (ii) the most likely path between two given graphons. It turns out that the addition of dynamics leads to new phenomena which are caused by bifurcations that occur in the solutions of associated variational problems. The talk does not assume any prior knowledge of graphons or large deviation theory.

The abstract is also available on the web-page of APSPS
                         https://sites.google.com/view/apsps/home<https://apc01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fsites.google.com%2Fview%2Fapsps%2Fhome&data=05%7C01%7Calejandro.freryorgambide%40vuw.ac.nz%7Ce404fe5887314a5bf6c008da5f2173ae%7Ccfe63e236951427e8683bb84dcf1d20c%7C0%7C0%7C637926894533842593%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=YZQC6NoqPxmWLhvqcwEOWnYCR%2BVJis1ojNFAHL1CZT0%3D&reserved=0>

We will open Zoom meeting soon after 5:00 pm, and the seminar presentation will start at 5:30pm NZ Time

Topic: APSPS#21
Time: Jul 13, 2022 05:00 PM Auckland, Wellington

Join from PC, Mac, iOS or Android:

https://vuw.zoom.us/j/91629520621<https://apc01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fvuw.zoom.us%2Fj%2F91629520621&data=05%7C01%7Calejandro.freryorgambide%40vuw.ac.nz%7Ce404fe5887314a5bf6c008da5f2173ae%7Ccfe63e236951427e8683bb84dcf1d20c%7C0%7C0%7C637926894533999982%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=H7QNk%2FhR9THdYNOcwpv2jP7ZlcnZPgBnZWHiBuLXEX8%3D&reserved=0>

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