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math.PR2025
Co-evolving vertex and edge dynamics in dense graphs
Siva Athreya, Frank den Hollander, Adrian Röllin
We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the o…
math.PR2024
Analytically weak and mild solutions to stochastic heat equation with irregular drift
Siva Athreya, Oleg Butkovsky, Khoa Lê +1
Consider the stochastic heat equation \begin{equation*} \partial_t u_t(x)=\frac12 \partial^2_{xx}u_t(x) +b(u_t(x))+\dot{W}_{t}(x),\quad t\in(0,T],\, x\in D, \end{equation*} where $…
math.PR2024
The Moran model with random resampling rates
Siva Athreya, Frank den Hollander, Adrian Röllin
In this paper we consider the two-type Moran model with individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution ${\mathb…