39 citations · 123 across the 23 of their papers we have counts for
27 papers
Condensed Ricci Curvature of Complete and Strongly Regular Graphs
Vincent Bonini, Conor Carroll, Uyen Dinh +3
We study a modified notion of Ollivier's coarse Ricci curvature on graphs introduced by Lin, Lu, and Yau in [11]. We establish a rigidity theorem for complete graphs that shows a c…
The irrationality measure of as seen through the eyes of
Sully F. Chen, Erin P. J. Pearse
For different values of , analysis of the end behavior of the sequence yields a strong connection to the irrationality measure of . We show that…
On the continuity of entropy of Lorenz maps
Zoe Cooperband, Erin P. J. Pearse, Blaine Quackenbush +3
We consider a one parameter family of Lorenz maps indexed by their point of discontinuity and constructed from a pair of bilipschitz functions. We prove that their topological…
Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks
Palle E. T. Jorgensen, Erin P. J. Pearse
We provide a streamlined construction of the Friedrichs extension of a densely-defined self-adjoint and semibounded operator on a Hilbert space , by means of a sym…
Symmetric pairs of unbounded operators in Hilbert space, and their applications in mathematical physics
Palle E. T. Jorgensen, Erin P. J. Pearse
In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In brief, a symmetric pair…
Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications
Palle Jorgensen, Erin Pearse, Feng Tian
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fix…
Unbounded containment in the energy space of a network and the Krein extension of the energy Laplacian
Palle E. T. Jorgensen, Erin P. J. Pearse
We compare the space of square-summable functions on an infinite graph (denoted ) with the space of functions of finite energy (denoted ). The…
Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable
Sabrina Kombrink, Erin P. J. Pearse, Steffen Winter
A long-standing conjecture of Lapidus claims that under certain conditions, self-similar fractal sets fail to be Minkowski measurable if and only if they are of lattice type. The t…
Iterated geometric harmonics for data imputation and reconstruction of missing data
Chad Eckman, Jonathan A. Lindgren, Erin P. J. Pearse +2
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synt…
Spectral comparisons between networks with different conductance functions
Palle E. T. Jorgensen, Erin P. J. Pearse
For a network consisting of a graph with edge weights prescribed by a given conductance function , we consider the effects of replacing these weights with a new function tha…
Self-similar fractals as boundaries of networks
Erin P. J. Pearse
For a given pcf self-similar fractal, a certain network (weighted graph) is constructed whose ideal boundary is (homeomorphic to) the fractal. This construction is the first repres…
Minkowski measurability results for self-similar tilings and fractals with monophase generators
Michel L. Lapidus, Erin P. J. Pearse, Steffen Winter
In a previous paper [arXiv:1006.3807], the authors obtained tube formulas for certain fractals under rather general conditions. Based on these formulas, we give here a characteriza…
Self-adjoint extensions of network Laplacians and applications to resistance metrics
Palle E. T. Jorgensen, Erin P. J. Pearse
Let be an infinite network, and let be the canonical energy form. Let be the Laplace operator with dense domain in and let …
Multiplication operators on the energy space
Palle E. T. Jorgensen, Erin P. J. Pearse
This paper studies the "energy space" (the Hilbert space of functions of finite energy, aka the Dirichlet-finite functions) on an infinite network (weig…
Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators
Michel L. Lapidus, Erin P. J. Pearse, Steffen Winter
In a previous paper by the first two authors, a tube formula for fractal sprays was obtained which also applies to a certain class of self-similar fractals. The proof of this formu…
Spectral reciprocity and matrix representations of unbounded operators
Palle E. T. Jorgensen, Erin P. J. Pearse
Motivated by potential theory on discrete spaces, we study a family of unbounded Hermitian operators in Hilbert space which generalize the usual graph-theoretic discrete Laplacian.…
Resistance boundaries of infinite networks
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a connected graph . The conductance function weights the edges, which are then interpreted as conductors of possibly varying strengths. The…
Gel'fand triples and boundaries of infinite networks
Palle E. T. Jorgensen, Erin P. J. Pearse
We study the boundary theory of a connected weighted graph from the viewpoint of stochastic integration. For the Hilbert space \HE of Dirichlet-finite functions on , we cons…
A Hilbert space approach to effective resistance metric
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a connected graph . The conductance function weights the edges, which are then interpreted as conductors of possibly varying strengths. The…
A discrete Gauss-Green identity for unbounded Laplace operators and transience of random walks
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a connected graph . The conductance function weights the edges, which are then interpreted as resistors of possibly varying strengths. The r…
The resolvent kernel for PCF self-similar fractals
Marius Ionescu, Erin P. J. Pearse, Luke G. Rogers +2
For the Laplacian defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also w…
Geometry of canonical self-similar tilings
Erin P. J. Pearse, Steffen Winter
We give several different geometric characterizations of the situation in which the parallel set of a self-similar set can be described by the inner -parallel set $T_{…
Operator theory of electrical resistance networks
Palle E. T. Jorgensen, Erin P. J. Pearse
A resistance network is a weighted graph with intrinsic (resistance) metric . We embed the resistance network into the Hilbert space of funct…
Tube formulas for self-similar fractals
Michel L. Lapidus, Erin P. J. Pearse
Tube formulas (by which we mean an explicit formula for the volume of an -neighbourhood of a subset of a suitable metric space) have been used in many situations to study proper…