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pro vyhledávání: '"Starr, Shannon"'
Autor:
Starr, Shannon
The Hardy-Ramanujan partition function asymptotics is a famous result in the asymptotics of combinatorial sequences. It was originally derived using complex analysis and number-theoretic ideas by Hardy and Ramanujan. It was later re-derived by Paul E
Externí odkaz:
http://arxiv.org/abs/2408.08269
Autor:
Wu, Erik, Starr, Shannon
In this short note we consider the computational problem of numerically finding the minimum and arg-min of a Brownian bridge. Using well-known results by Pitman, Tanaka, Vervaat and Williams we are able to show that the bisection method has both a sm
Externí odkaz:
http://arxiv.org/abs/2407.19490
Autor:
Hossein, Samen, Starr, Shannon
Given $\pi \in S_n$, let $Z_{n,k}(\pi)=\sum_{1\leq i_1<\dots
Externí odkaz:
http://arxiv.org/abs/2404.05860
Autor:
Starr, Shannon, Wu, Erik
The distribution for the minimum of Brownian motion or the Cauchy process is well-known using the reflection principle. Here we consider the problem of finding the sample-by-sample minimum, which we call the online minimum search. We consider the pos
Externí odkaz:
http://arxiv.org/abs/2312.17705
For the quantum Heisenberg antiferromagnet with spin-$j$ on a bipartite, balanced graph, the Lieb-Mattis theorem, ``Ordering of energy levels,'' guarantees that the ground state is a spin singlet, and moreover, defining $E^{\textrm{AF}}_{\min}(S)$ to
Externí odkaz:
http://arxiv.org/abs/2307.12773
Autor:
Hossein, Samen, Starr, Shannon
Given a uniform random permutation $\pi \in S_n$, let $Z_{n,k}$ be equal to the number of increasing subsequences of length $k$: so $Z_{n,k}=|\{(i_1,\dots,i_k) \in \mathbb{Z}^k\, :\, 1\leq i_1<\dots
Externí odkaz:
http://arxiv.org/abs/2301.00125
Autor:
Froehlich, Michael, Starr, Shannon
We consider two examples for a well-known method for obtaining concentration of measure (COM) bounds for a given observable in a given measure. The method is to consider an auxiliary Markov chain for which the invariant distribution is the measure of
Externí odkaz:
http://arxiv.org/abs/1901.08410
Autor:
Starr, Shannon, Williams, Scott
We summarize how to obtain rough bounds for one version of the emptiness formation probability in the 2d dimer model. The methods we use are the same as have been developed to obtain EFP bounds in the 1d XXZ model in a paper with Crawford, Ng and one
Externí odkaz:
http://arxiv.org/abs/1810.08846
We prove a result for the spin-$1/2$ quantum Heisenberg ferromagnet on $d$-dimensional boxes $\{1,\dots,L\}^d \subset \mathbb{Z}^d$. For any $n$, if $L$ is large enough, the Hamiltonian satisfies: among all vectors whose total spin is at most $(L^d/2
Externí odkaz:
http://arxiv.org/abs/1509.00907
Autor:
Starr, Shannon, Walters, Meg
For a positive number $q$ the Mallows measure on the symmetric group is the probability measure on $S_n$ such that $P_{n,q}(\pi)$ is proportional to $q$-to-the-power-$\mathrm{inv}(\pi)$ where $\mathrm{inv}(\pi)$ equals the number of inversions: $\mat
Externí odkaz:
http://arxiv.org/abs/1502.03727