21 citations · 55 across the 14 of their papers we have counts for
17 papers
The Opdam-Cherednik kernel is the Laplace transform of a positive measure
Colin McSwiggen, Siddhartha Sahi
We prove that the Opdam-Cherednik kernel, also known as the nonsymmetric Opdam hypergeometric function, can be written as the Laplace transform of a positive measure supported on t…
The Rectangular Finite Free Heat Flow
Cesar Cuenca, Colin McSwiggen
We define and study the rectangular finite free heat flow, a dynamical system on polynomials that plays the role of the heat equation in the setting of rectangular finite free prob…
Majorization Inequalities from Logarithmic Convexity
Colin McSwiggen, Siddhartha Sahi
Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Baudhāyana's Śu…
Topological Obstructions to Shared Priors
Owen D. Biesel, Colin McSwiggen, Ted Theodosopoulos +1
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as c…
On the limiting Horn inequalities
Samuel G. G. Johnston, Colin McSwiggen
The Horn inequalities characterise the possible spectra of triples of -by- Hermitian matrices . We study integral inequalities that arise as limits of Horn inequalitie…
How Flawed Is ECE? An Analysis via Logit Smoothing
Muthu Chidambaram, Holden Lee, Colin McSwiggen +1
Informally, a model is calibrated if its predictions are correct with a probability that matches the confidence of the prediction. By far the most common method in the literature f…
Asymptotics of Generalized Bessel Functions and Weight Multiplicities via Large Deviations of Radial Dunkl Processes
Jiaoyang Huang, Colin McSwiggen
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation th…
Moments of random quantum marginals via Weingarten calculus
Sho Matsumoto, Colin McSwiggen
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a…
Projections of Orbital Measures and Quantum Marginal Problems
Benoît Collins, Colin McSwiggen
This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix…
Sampling Matrices from Harish-Chandra-Itzykson-Zuber Densities with Applications to Quantum Inference and Differential Privacy
Jonathan Leake, Colin S. McSwiggen, Nisheeth K. Vishnoi
Given two Hermitian matrices and , the Harish-Chandra-Itzykson-Zuber (HCIZ) distribution on the unitary group is , whe…
Majorization and Spherical Functions
Colin McSwiggen, Jonathan Novak
Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In thi…
Box splines, tensor product multiplicities and the volume function
Colin McSwiggen
We study the relationship between the tensor product multiplicities of a compact semisimple Lie algebra and a special function associated to $\mathfrak…
Revisiting Horn's Problem
Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the class…
On Horn's Problem and its Volume Function
Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber
We consider an extended version of Horn's problem: given two orbits and of a linear representation of a compact Lie group, let ,…
The Harish-Chandra integral: An introduction with examples
Colin McSwiggen
This expository paper introduces the theory of Harish-Chandra integrals, a family of special functions that express the integral of an exponential function over the adjoint orbits…
A new proof of Harish-Chandra's integral formula
Colin McSwiggen
We present a new proof of Harish-Chandra's formula $$Π(h_1) Π(h_2) \int_G e^{\langle \mathrm{Ad}_g h_1, h_2 \rangle} dg = \frac{ [ \! [ Π, Π] \!] }{|W|} \sum_{w \in W} ε(w) e^{\lan…
Visualizing the "Heartbeat" of a City with Tweets
Urbano França, Hiroki Sayama, Colin McSwiggen +2
Describing the dynamics of a city is a crucial step to both understanding the human activity in urban environments and to planning and designing cities accordingly. Here we describ…