arXiv subjects

Sudheesh Surendranath

Publications and source records attributed to Sudheesh Surendranath.

3 recordsLinked to original sources

arXiv2026

Continuous-time directed polymers to the Critical SHF via moments

We consider a class of two-dimensional continuous-time directed random polymers in a correlated Brownian environment. The partition functions of these polymers form a discrete approximation of the Critical Stochastic Heat Flow (SHF), constructed by Caravenna, Sun and Zygouras (2023). Using a recent moment based axiomatic characterization of the SHF by Tsai (2024), we prove that the point-to-point partition functions, viewed as random measures, converge to the critical SHF. The proof proceeds by first establishing convergence of all moments through the resolvent method introduced by Gu, Quastel and Tsai (2021) and based on Rajeev (1999) and Dimock and Rajeev (2004). This is followed by establishing tightness and verifying the remaining axioms in the characterization.

math.PR↗

arXiv2025

Hölder regularity for a class of nonlinear stochastic heat equations

We investigate the Hölder continuity of solutions to stochastic partial differential equations of the form $\frac{\partial u}{\partial t}=\mathcal{L}u+σ(u)\dot{F}$, subject to a suitable initial condition. The noise term $\dot{F}$ is white in time, colored in space, and $\mathcal{L}$ is the $\mathcal{L}^{2}$-generator of a Lévy process. Under a growth assumption on the characteristic exponent of the Lévy process, we derive sufficient conditions for the solution to be locally Hölder continuous. Moreover, we show that these conditions are equivalent to those derived in related papers by Khoshnevisan-Sanz-Solé (2023) and Sanz-Solé-Sarrá (2000, 20002).

math.PR↗

arXiv2025

Two dimensional delta Bose gas in a weighted space

We extend the construction of the semigroup of the two-dimensional delta-Bose gas in Gu, Quastel, and Tsai (2021) (based on Rajeev (1999) and Dimock and Rajeev (2004)) to a weighted $L^2$ space that allows exponentially growing functions. We further show that the semigroup of the mollified delta-Bose gas converges strongly to that of the delta-Bose gas.

math.PR↗