Probability Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- 1043 in Sidney Lu Mechanical Engineering Building
- Date
- Jul 23, 2024 2:00 - 2:50 pm
- Speaker
- Zhenyao Sun (Beijing Institute of Technology)
- Contact
- Renming Song
- rsong@illinois.edu
- Views
- 62
- Originating Calendar
- Probability Research Area Calendar
Title: From stochastic heat equations to Arratia flow.
Abstract: Consider the 1-D stochastic heat equation with transport noise:
dvt = 1/2 ∆vtdt+αε(∇vt)dWtε, t≥0,x∈R
and the 1-D stochastic heat equation with multiplicative conservative noise:
dut = 1/2 ∆utdt+αε ∇(utdWtε), t≥0,x∈R.
Assume that Wtε = Wt∗ hε is the spatial convolution between the cylindrical Wiener process and a smooth compactly supported mollifier hε:=ε−1h(ε−1·). We show that when ε ↓ 0, the solutions (vtε)t≥0, and respectively (utε)t≥0, converge in distribution to the cumulative Arratia flow, and respectively, the massive Arratia flow when the noise strength αε is properly tuned. This is based on ongoing joint work with Xiaolong Zhang.