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Characterising long-term covid-19: a rapid living systematic review
Objective To understand the frequency, profile, and duration of persistent symptoms of covid-19 and to update this understanding as new evidence emerges. Design: A living systematic review producedExpand
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Analyticity for classical gasses via recursion
We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the boundExpand
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Central limit theorems and the geometry of polynomials
Let $X \in \{0,\ldots,n \}$ be a random variable, with mean $\mu$ and standard deviation $\sigma$ and let \[f_X(z) = \sum_{k} \mathbb{P}(X = k) z^k, \] be its probability generating function.Expand
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Central limit theorems from the roots of probability generating functions
For each $n$, let $X_n \in \{0,\ldots,n\}$ be a random variable with mean $\mu_n$, standard deviation $\sigma_n$, and let \[ P_n(z) = \sum_{k=0}^n \mathbb{P}( X_n = k) z^k ,\] be its probabilityExpand
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A Short Note on the Average Maximal Number of Balls in a Bin
  • M. Michelen
  • Mathematics, Computer Science
  • J. Integer Seq.
  • 22 May 2019
TLDR
We analyze the asymptotic behavior of the average maximal number of balls in a bin obtained by throwing uniformly at random $r$ balls without replacement into $n$ bins, $T$ times. Expand
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The frog model on Galton-Watson trees
We consider an interacting particle system on trees known as the frog model: initially, a single active particle begins at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles areExpand
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Maximum entropy and integer partitions
We derive asymptotic formulas for the number of integer partitions with given sums of jth powers of the parts for j belonging to a finite, non-empty set J ⊂ N. The method we use is based on theExpand
Asymptotic bounds on graphical partitions and partition comparability
An integer partition is called graphical if it is the degree sequence of a simple graph. We prove that the probability that a uniformly chosen partition of size $n$ is graphical decreases to zeroExpand
Quenched Survival of Bernoulli Percolation on Galton-Watson Trees
We explore the survival function for percolation on Galton-Watson trees. Letting $g(T,p)$ represent the probability a tree $T$ survives Bernoulli percolation with parameter $p$, we establish severalExpand
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PR ] 3 J un 2 01 8 Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees
We consider critical percolation on Galton-Watson trees and prove quenched analogues of classical theorems of critical branching processes. We show that the probability critical percolation reachesExpand