Pradeeptha R Jain | Searcharxiv

arXiv2026

Annealed Survival Probability of Random Walk in an Inhomogeneous Poisson Environment of Mobile Traps

We study the annealed survival probability of a random walk in an inhomogeneous Poisson environment of mobile traps on $\mathbb{Z}^d$. In dimensions $d=1,2$, we determine the asymptotics for the annealed survival probability of the walker under suitable assumptions on the average trap intensity and study how inhomogeneity in the initial trap configuration affects these asymptotics. Our results extend the asymptotics proved for the homogeneous setting in \cite{DGRS2012}. We also establish a law of large numbers, central limit theorem and large deviation principle for the inhomogeneous Poisson trap environment in $d\ge 1$, generalising the corresponding results proved for the homogeneous case considered in \cite{CG1984}. We present a class of examples of inhomogeneous trap environments where the decay rate of survival probability can be identified and also instances where it does not decay with time.

math.PR↗

arXiv2025

The Triangle Friendship Paradox

We consider the generalised friendship paradox, focussing on the number of triangles at a vertex as the relevant attribute. We show that, contrary to the setting where the attribute is the number of edges at a vertex or the number of wedges at a vertex, the average friendship-bias of the number of triangles at a vertex is not always non-negative. We identify classes of finite deterministic graphs for which the bias is non-negative, and provide examples of finite deterministic graphs for which it is not. For certain classes of sparse and dense random graphs, we compute the scaling of the bias in the limit as the number of vertices tends to infinity.

math.PR↗