arXiv subjects

Varun Kotharkar

Publications and source records attributed to Varun Kotharkar.

3 recordsLinked to original sources

arXiv2026

An Interpretable Low-Rank State-Space Model for Multi-Horizon Simulation of Large-Scale Regional Temperature Fields

We propose an interpretable low-rank state-space model for conditional simulation of daily regional temperature fields. The central statistical question is whether empirical orthogonal functions (EOFs) can be treated as stable large-scale features of the field rather than only as sample-dependent basis vectors for dimension reduction. The framework represents the dominant temperature field through a small number of retained EOF coefficients, models their seasonal mean and variance structure, propagates the resulting low-dimensional state with stable multivariate dynamics, and uses structured innovations to represent the remaining uncertainty. The resulting reduced-rank model is interpretable, computationally efficient, and suitable for iterative ensemble generation. It is designed to support both inference on the structure of the retained temperature state and prediction through multi-horizon probabilistic field simulation.

stat.ME↗

arXiv2026

LLY Ricci Reweighting in Stochastic Block Models: Uniform Curvature Concentration and Finite-Horizon Tracking

We study curvature-driven edge reweighting for community recovery in the balanced two-block stochastic block model. Given a graph G with initial weights equal to the adjacency matrix, we iteratively update edge weights using Lin-Lu-Yau (Ollivier-type) Ricci curvature, while all transportation costs are computed in the unweighted graph metric. In a moderate-density regime we prove uniform concentration of edge curvatures and show that a single Ricci reweighting step produces a two-level weighting that amplifies within-block connectivity relative to across-block connectivity. As a consequence, spectral clustering on the reweighted graph has a strictly larger population eigengap, and we obtain corresponding non-asymptotic perturbation bounds and Davis-Kahan misclustering guarantees. We further analyze a fixed finite horizon of iterated reweighting, where the random iterates track a deterministic two-weight recursion uniformly over the time horizon. This yields a principled finite-horizon curvature flow interpretation for community detection in a canonical random graph model.

cs.SI↗

arXiv2025

Fixed and Increasing Domain Asymptotics for the Roughness and Scale of Isotropic Gaussian Random Fields

We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main results are bivariate central limit theorems for a class of method-of-moments estimators under increasing-domain and fixed-domain asymptotics. The fixed-domain result follows immediately from the increasing-domain result from the self-similarity of Gaussian random fields with power-law generalized covariances \cite{IstasLang1997, Coeurjolly2001, ZhuStein2002}. These results provide a unified distributional framework across these two classical regimes \cite{AvramLeonenkoSakhno2010-ESAIM, BiermeBonamiLeon2011-EJP} that makes the unusual behavior of the estimates under fixed-domain asymptotics intuitively obvious. Our increasing-domain asymptotic results use spatial averages of quadratic forms of (iterated) bilinear product difference filters that yield explicit expressions for the estimates of roughness and scale to which existing theorems on such averages \cite{BreuerMajor1983,Hannan1970} can be readily applied. We further show that the asymptotics remain valid under modestly irregular sampling due to jitter or missing observations. For the fixed-domain setting, the results extend to models that behave sufficiently like the power-law model at high frequencies such as the often used Mat\'ern model \cite{ZhuStein2006, WangLoh2011EJS, KaufmanShaby2017EJS}.

math.ST↗