arXiv subjects

Sayantan Maitra

Publications and source records attributed to Sayantan Maitra.

2 recordsLinked to original sources

arXiv2025

The real layering field of Brownian loop soup and the Gaussian multiplicative chaos

We consider the random field defined by the layering numbers of the Brownian loop soup in a bounded simply connected domain in the complex plane. We call this the layering field and show that, after a suitable renormalization, it converges to the subcritical Gaussian multiplicative chaos. The main technique for our proof is the Wiener-Itô chaos expansion. We also calculate the $n$-point functions of the layering field, show their conformal covariance and discuss their behavior near the boundary of the domain.

math.PR↗

arXiv2022

Weak Uniqueness for the Stochastic Heat Equation Driven by a Multiplicative Stable Noise

We consider the stochastic heat equation $$\frac{\partial Y_t(x)}{\partial t} = \frac{1}{2} Δ_x Y_t(x) + Y_{t-}(x)^β \dot{L}^α$$ with $t \ge 0$, $x \in \mathbb{R}$ and $L^α$ being an $α$-stable white noise without negative jumps. Under appropriate non-negative initial conditions, when $α\in (1,2)$ and $β\in (\frac{1}α, 1)$ we prove that weak uniqueness holds for the above using the approximating duality approach developed by Mytnik (Ann. Probab. (1998) 26 968-984).

math.PR↗