Tootfinder

Observables of random spanning trees in random environment
Luca Makowiec
https://arxiv.org/abs/2507.07702 https://arxiv.org/pdf/2507.…

Observables of random spanning trees in random environment
In this thesis, we study a new disordered system called random spanning tree in random environment (RSTRE) across different families of graphs with varying disorder distributions. We examine several observables as functions of the disorder strength (inverse temperature) $β\geq 0$, and compare their values to the extreme cases $β= 0$ and $β\rightarrow \infty$, which correspond to the uniform spanning tree (UST) and the minimum spanning tree (MST), respectively. The results concerning the diam…

Simulated prosthetic vision confirms checkerboard as an effective raster pattern for epiretinal implants https://iopscience.iop.org/article/10.1088/1741-2552/adecc4 on sequential activation of subsets of electrodes; "Random patterns resulted in the lowest performance&qu…

A c-theorem for the effective central charge in the R=1 replica limit, and applications to systems with measurement-induced randomness
Rushikesh A. Patil, Andreas W. W. Ludwig
https://arxiv.org/abs/2507.07959

A c-theorem for the effective central charge in the R=1 replica limit, and applications to systems with measurement-induced randomness
We present a general theorem demonstrating non-perturbatively the decrease of the "effective central charge" $c_{\text{eff}}=(d c/dR)|_{R=1}$ under renormalization group (RG) flow in the $R\rightarrow1$ replica limit of a $R$-copy $2D$ conformal field theory (CFT) action $S_{*}$ perturbed by a replica interaction of the form $$-\mathbb{S}=-\sum_{a=1}^{R}S_{*}^{(a)}+Δ\int d^2 x \sum_{\substack{a,b=1\\ a\neq b}}^{R}φ^{(a)}(x)φ^{(b)}(x).$$ Here $φ$ is a scaling field belonging to the CFT …

Random #git tip: if you need to push a commit to restart a #CI / #CD workflow that you can't restart directly, you can use:
git commit --allow-empty
instead of making meaningless changes.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer
Christopher D. Sinclair, Jonathan M. Wells
https://arxiv.org/abs/2509.05487 https://

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer
We give a hyperpfaffian formulation for correlation functions in $β$-ensembles of $M \times M$ random matrices when $β= L^2$ is an even square integer. More specifically, to the $m$th correlation function $R_m : \R^m \rightarrow [0, \infty)$ we associate the $L$-vector valued function $ω_m : \R^m \rightarrow Λ^L \R^{L(M-m)}$ such that $R_m(\mathbf y)$ is given by the Vandermonde determinant in $y_1, \ldots, y_M$ times the hyperpfaffian of $ω_m.$ The partition function of the ensemble was p…

On the recognition problem for limits of entropy functions
Geva Yashfe
https://arxiv.org/abs/2509.06302 https://arxiv.org/pdf/2509.06302

On the recognition problem for limits of entropy functions
We prove that there is no algorithm to decide whether a given integer vector is in the closure of the entropic cone $\overline{Γ_{n}^{*}}$. Equivalently, there is no decision procedure to determine whether a given integer-valued function $h:\mathcal{P}(\{1,\ldots,n\})\rightarrow\mathbb{Z}_{\ge 0}$ is a pointwise limit of joint entropy functions. In other words, given such an $h$, it is undecidable whether for all $\varepsilon > 0$ there exists a finite probability space $(Ω,P)$ with random va…

A Simple and Robust Protocol for Distributed Counting
Edith Cohen, Moshe Shechner, Uri Stemmer
https://arxiv.org/abs/2509.05870 https://arxiv.org/pdf/2509.…

A Simple and Robust Protocol for Distributed Counting
We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across $k$ sites while minimizing communication. The communication complexity of this problem is known to be $Θ(\frac{k}ε\log N)$ for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to $Θ(\frac{\sqrt{k}}ε\log N)$, but their analysis is restricted to the {\em oblivious setting}, where the stream of events is independent …

Treatment effect extrapolation in the presence of unmeasured confounding
Stephanie Riley, Ricardo Silva, Matthew Sperrin
https://arxiv.org/abs/2509.06045 https://

Treatment effect extrapolation in the presence of unmeasured confounding
While randomised controlled trials (RCTs) are the gold standard for estimating causal treatment effects, their limited sample sizes and restrictive criteria make it difficult to extrapolate to a broader population. Observational data, while larger, suffer from unmeasured confounding. Therefore, we can combine the strengths of both data sources for more accurate results. This work extends existing methods that use RCTs to debias conditional average treatment effects (CATEs) estimated in observ…

Restricted Quasiconvexity Isometry Property for Symmetric $\alpha$-Stable Random Matrices
Sunder Ram Krishnan
https://arxiv.org/abs/2507.02649 https://

Restricted Quasiconvexity Isometry Property for Symmetric $α$-Stable Random Matrices
We formulate a generalization of the Restricted Isometry Property (RIP) referred to as the Restricted Quasiconvexity Isometry Property (RQIP) for alpha stable random projections with $0<α<1$. A lower bound on the number of rows for RQIP to hold for random matrices whose entries are drawn from a symmetric $α$-stable ($SαS$) distribution is derived. The proof leverages two key components: a concentration inequality for empirical fractional moments of $SαS$ variables and a covering number boun…

Approximation of the L\'evy-driven stochastic heat equation on the sphere
Annika Lang, Andrea Papini, Verena Schwarz
https://arxiv.org/abs/2507.05005 h…

Approximation of the Lévy-driven stochastic heat equation on the sphere
The stochastic heat equation on the sphere driven by additive Lévy random field is approximated by a spectral method in space and forward and backward Euler-Maruyama schemes in time, in analogy to the Wiener case. New regularity results are proven for the stochastic heat equation. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. To do so, we restrict to square-integrable random field and optimal strong convergence rat…