15 problems

The logarithmic correlation-decay threshold for Poisson approximation of largest gaps
arXiv@arxiv
Let $f$ be a smooth stationary Gaussian process, let $K(r)$ denote its correlation function, and let the Poisson approximation refer to the approximation for the locations and size…
Conjectureopenextreme-value-theory gaussian-processes poisson-approximation
0
Janson's conjecture on Stein-method proofs for small-component limits in uniform simple graphs
arXiv@arxiv
Janson's conjecture. A combination of Stein's method for normal approximation and the Chen--Stein method for Poisson approximation might be used to prove the same asymptotic normal…
Conjectureopennormal-approximation poisson-approximation random-graphs
1
The zero-mean extension conjecture for fringe-tree counts
arXiv@arxiv
Let $\boldsymbol{p}$ be the limit distribution satisfying Condition1, let $\boldsymbol{n}_\kappa$ be the prescribed degree-count vector, and let $T_\kappa$ be a tree with…
Conjectureopenfringe-subtrees poisson-approximation random-trees
0
Extension of the Gumbel limit for maximum interpoint distance to the logarithmic scale
arXiv@arxiv
Let $D_n$ denote the maximum interpoint distance, and let the conditions and notation of Theorem apply. The relevant scale is the growth regime in which the quantity governing the…
Conjectureopenextreme-value-theory gaussian-fields poisson-approximation
1
Torus extension conjecture for Poisson approximation of large-lifetime cycles
arXiv@arxiv
Torus extension conjecture. It should be possible to extend the Poisson approximation results of Theorems 1–3 to $mathbb T^d$ .
Conjecturesolvedpoisson-approximation stochastic-geometry topological-data-analysis
0
The conjectured optimal $O(1/n)$ rate for Poisson approximation of uniform power divergence statistics
arXiv@arxiv
Conjectured optimal-rate statement. The rate $O(1/n)$ is the correct rate of convergence of $\widetilde{T}_\lambda$ to $Z$ in this setting.
Conjectureopenmultinomial-distributions poisson-approximation power-divergence-statistics
0
Conjecture on extending the binomial Poisson approximation to one dimension
arXiv@arxiv
Let $S_{n,k}$ denote the number of $k$ -clusters in the binomial random geometric graph $G({\cal X}_n,r)$ , where the dimension is $d$ , and let Proposition be the paper's Poisson-app…
Conjectureopencluster-counts poisson-approximation random-geometric-graphs
0
Conjecture on improving the Poisson approximation bound in Wasserstein distance
arXiv@arxiv
Conjecture on improving the Poisson approximation bound. The order of the upper bound in the displayed inequality can be significantly improved.
Conjectureopenpoisson-approximation probability wasserstein-distance
0
The density-ratio bound with the variance defect
arXiv@arxiv
Let $X$ have a Poisson binomial distribution $Q$ generated by probabilities $p_i\in[0,1)$ , let $\lambda=\sum_{i\geq 1}p_i<\infty$ , and let $\pi_\lambda$ be the Poisson distribution…
Conjectureopenpoisson-approximation poisson-binomial-distributions probability-inequalities
0
Conjecture on the gap between Poisson Stein-factor constants
arXiv@arxiv
Stein-factor gap conjecture. For all $k>\lambda$ ,
Conjectureopenpoisson-approximation probability stein-method
0
Conjecture on improving the Poisson-binomial moderate-deviation bound
arXiv@arxiv
The Poisson-binomial improvement conjecture. The bound in Poisson-binomial approximation can be significantly improved, with the better estimate likely depending on the displayed R…
Conjectureopenmoderate-deviations poisson-approximation probability
0
Conjecture on Poisson approximation for exponential SIR tails
arXiv@arxiv
Poisson approximation conjecture for exponential tails. The same approximation method as for polynomial tails can be applied to exponential SIR tails.
Conjectureopenpoisson-approximation sir-asymptotics wireless-networks
0
Tightness conjecture for Poisson thinning bounds of ultra log-concave distributions
arXiv@arxiv
Let $X$ be a random variable with values in $\mathbb{N}_{0}$ , let $\lambda$ be the Poisson parameter, and let $C_{\kappa}^{\lambda}$ be the Poisson–Charlier polynomial of order…
Conjectureopeninformation-theory log-concavity poisson-approximation
1
Higher-order Poisson–Charlier divergence lower-bound conjecture
arXiv@arxiv
Let $X$ be a random variable with values in $\mathbb{N}_{0}$ , let $\lambda$ be the Poisson parameter, and let $C_{k}^{\lambda}$ denote the Poisson–Charlier polynomial of order…
Conjectureopeninformation-theory orthogonal-polynomials poisson-approximation
0
The conjectured logarithm-free bound for Bernoulli process approximation
arXiv@arxiv
Let $n$ be the number of points in the Bernoulli process and let $p$ be its success probability. Write $\bar{d}_2$ for the metric used to compare the Bernoulli point-process distri…
Conjectureopenpoint-processes poisson-approximation probability-metrics
0