Related papers: Sharp threshold for the Ising perceptron model
Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NP-complete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries…
We have performed a search for scalar top quark (stop) pair production in the inclusive electron-muon-missing transverse energy final state, using a sample of $p \bar{p}$ events corresponding to 108.3 pb$^{-1}$ of data collected with the…
We show that in the Ising pure $p$-spin model of spin glasses, shattering takes place at all inverse temperatures $\beta \in (\sqrt{(2 \log p)/p}, \sqrt{2\log 2})$ when $p$ is sufficiently large as a function of $\beta$. Of special interest…
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop…
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…
We explore the phenomenology of three Higgs doublet scenario, where the scalar potential is augmented by $\mathbb{Z}_{3} \times \mathbb{Z}_{2}$ symmetry making one doublet inert. Thus in effect, our model of interest is two Higgs plus inert…
We investigate a scenario inspired by natural supersymmetry, where neutrino data is explained within a low-scale seesaw scenario. For this the Minimal Supersymmetric Standard Model is extended by adding light right-handed neutrinos and…
We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods.…
Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated…
Consider a pair of correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,\tfrac{\lambda}{n};s)$ that are subsampled from a common parent Erd\H{o}s-R\'enyi graph with average degree $\lambda$ and subsampling probability $s$. We establish a sharp…
We study the connectivity of random subgraphs of the $d$-dimensional Hamming graph $H(d, n)$, which is the Cartesian product of $d$ complete graphs on $n$ vertices. We sample the random subgraph with an i.i.d.\ Bernoulli bond percolation on…
We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we…
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…
This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of our analysis, we use generic chaining techniques to obtain…
Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for…
Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of $n^{-1/2}$ in the uniform metric, in other words, when…
For several types of correlations: mixed-state entanglement in systems of distinguishable particles, particle entanglement in systems of indistinguishable bosons and fermions and non-Gaussian correlations in fermionic systems we estimate…
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…
We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the…
We investigate the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent $\Phi$,…