1 citations · 1 across the 6 of their papers we have counts for
6 papers
Urschel Nodal Domains via Perturbation Theory
Joel Friedman, Tong Ling, Soumyajit Saha
We prove several types of Courant nodal domain theorems for generalized Laplacians on graphs, based on an invariant introduced by Urschel, which we call the "Urschel number", denot…
Nodal Domains on Surfaces under Perturbation: Upper Semicontinuity, Courant-Sharpness, and Boundary Intersections
Saikat Maji, Mayukh Mukherjee, Soumyajit Saha
We study how the number of nodal domains of eigenfunctions of Schrödinger operators on closed surfaces changes under smooth perturbations of along conver…
Eigenfunction localization and nodal geometry on dumbbell domains
Saikat Maji, Soumyajit Saha
In this article, we study the location of the first nodal line and hot spots under different boundary conditions on dumbbell-shaped domains. Apart from its intrinsic interest, dumb…
Sharp lower bound on the "number of nodal decomposition" of graphs
Hiranya Kishore Dey, Soumyajit Saha
Urschel introduced a notion of nodal partitioning to prove an upper bound on the number of nodal decomposition of discrete Laplacian eigenvectors. The result is an analogue to the…
Heat profile, level sets and hot spots of Laplace eigenfunctions
Mayukh Mukherjee, Soumyajit Saha
We use probabilistic tools based on Brownian motion and Feynman-Kac formulae to investigate the heat profile for the ground state Dirichlet and second Neumann eigenfunctions. Among…
On the effects of small perturbation on low energy Laplace eigenfunctions
Mayukh Mukherjee, Soumyajit Saha
We investigate several aspects of the nodal geometry and topology of Laplace eigenfunctions, with particular emphasis on the low frequency regime. This includes investigations in a…