Publications (23)
On the Approximability of Time Disjoint Walks
Alexandre Bayen, Jesse Goodman, Eugene Vinitsky
We introduce the combinatorial optimization problem Time Disjoint Walks (TDW), which has applications in collision-free routing of discrete objects (e.g., autonomous vehicles) over…
Invasion percolation on regular trees
Omer Angel, Jesse Goodman, Frank den Hollander +1
We consider invasion percolation on a rooted regular tree. For the infinite cluster invaded from the root, we identify the scaling behavior of its -point function for any $r\geq…
A general framework for computation and estimation using the saddlepoint approximation
Godrick Oketch, Rachel M. Fewster, Jesse Goodman
The saddlepoint approximation provides highly accurate approximations to probability density and mass functions using only the corresponding moment generating functions (MGFs). Rec…
An atomic decomposition of one-dimensional metric currents without boundary
You-Wei Benson Chen, Jesse Goodman, Felipe Hernandez +1
This paper proves an atomic decomposition of the space of -dimensional metric currents without boundary, in which the atoms are specified by closed Lipschitz curves with uniform…
Leakage-Resilient Extractors against Number-on-Forehead Protocols
Eshan Chattopadhyay, Jesse Goodman
Given a sequence of independent sources , how many of them must be good (i.e., contain some min-entropy) in order to…
What is the price of approximation? The saddlepoint approximation to a likelihood function
Godrick Oketch, Rachel M. Fewster, Jesse Goodman
The saddlepoint approximation to the likelihood, and its corresponding maximum likelihood estimate (MLE), offer an alternative estimation method when the true likelihood is intract…
Potential Estimates and Hodge Systems with data on compact manifolds
Jesse Goodman, Felipe Hernández, Daniel Spector
In this paper we establish optimal Lorentz estimates for the Riesz potentials acting on closed or co-closed -forms of finite mass on a smooth, compact Riemannian manifold of dim…
Low-Degree Polynomials Extract from Local Sources
Omar Alrabiah, Eshan Chattopadhyay, Jesse Goodman +2
We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in…
Extractors for Polynomial Sources over
Eshan Chattopadhyay, Jesse Goodman, Mohit Gurumukhani
We explicitly construct the first nontrivial extractors for degree polynomial sources over . Our extractor requires min-entropy $k\geq n - \tildeΩ(\sqrt{…
Scaling limit of the invasion percolation cluster on a regular tree
Omer Angel, Jesse Goodman, Mathieu Merle
We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height funct…
Exponential growth of ponds in invasion percolation on regular trees
Jesse Goodman
In invasion percolation, the edges of successively maximal weight (the outlets) divide the invasion cluster into a chain of ponds separated by outlets. On the regular tree, the pon…
Improved Condensers for Chor-Goldreich Sources
Jesse Goodman, Xin Li, David Zuckerman
One of the earliest models of weak randomness is the Chor-Goldreich (CG) source. A -CG source is a sequence of random variables , where…
Properties of the Affine Invariant Ensemble Sampler in high dimensions
David Huijser, Jesse Goodman, Brendon J. Brewer
We present theoretical and practical properties of the affine-invariant ensemble sampler Markov chain Monte Carlo method. In high dimensions the affine-invariant ensemble sampler s…
Short paths for first passage percolation on the complete graph
Maren Eckhoff, Jesse Goodman, Remco van der Hofstad +1
We study the complete graph equipped with a topology induced by independent and identically distributed edge weights. The focus of our analysis is on the weight W_n and the number…
Improved Extractors for Small-Space Sources
Eshan Chattopadhyay, Jesse Goodman
We study the problem of extracting random bits from weak sources that are sampled by algorithms with limited memory. This model of small-space sources was introduced by Kamp, Rao,…
Lectures on Self-Avoiding Walks
Roland Bauerschmidt, Hugo Duminil-Copin, Jesse Goodman +1
These lecture notes provide a rapid introduction to a number of rigorous results on self-avoiding walks, with emphasis on the critical behaviour. Following an introductory overview…
Two Approximation Results for Divergence Free Measures
Jesse Goodman, Felipe Hernandez, Daniel Spector
In this paper we prove two approximation results for divergence free measures. The first is a form of an assertion of J. Bourgain and H. Brezis concerning the approximation of sole…
Extremal geometry of a Brownian porous medium
Jesse Goodman, Frank den Hollander
The path W[0,t] of a Brownian motion on a d-dimensional torus T^d run for time t is a random compact subset of T^d. We study the geometric properties of the complement T^d \ W[0,t]…
The saddlepoint approximation factors over sample paths of recursively compounded processes
Jesse Goodman
This paper presents an identity between the multivariate and univariate saddlepoint approximations applied to sample path probabilities for a certain class of stochastic processes.…
Low-Degree Polynomials Are Good Extractors
Omar Alrabiah, Jesse Goodman, Jonathan Mosheiff +1
We prove that random low-degree polynomials (over ) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomne…
Asymptotic accuracy of the saddlepoint approximation for maximum likelihood estimation
Jesse Goodman
The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself t…
Degree distribution of shortest path trees and bias of network sampling algorithms
Shankar Bhamidi, Jesse Goodman, Remco van der Hofstad +1
In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determi…
Some remarks on boundary operators of Bessel extensions
Jesse Goodman, Daniel Spector
In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is \[Î_x u(x,y) +\frac{1-2s}{y} \frac{\partial u}{\partial y}(…