8 problems

Density-free heavy-traffic limit conjecture. The density condition is not needed for the heavy-traffic limit theorem: under the remaining hypotheses, $\{\nu^{(n)}\}$ converges weak…

The BAR approach refers to deriving diffusion limits of stationary distributions using the stationary equation and a test function. In the history-dependent M/M/1 queue framework,…

Let $\boldsymbol{h}^{G_n(t)}$ denote the opinion-density process on the dynamic random graph $G_n$, let $\beta>0$ be the model parameter, and let $\boldsymbol{h}^{G_n(nt)}$ be the…

The expected squared jump distance scaling constant $h(\ell)$ is defined by … where $\Phi$ is the standard Normal cumulative distribution function and $\ell$ is the limiting rescal…

Let $G(\frac{1}{n}\gamma^{(n)})$ converge in distribution, with respect to the Hausdorff metric, to a compact set of positive Lebesgue measure. Convergence-extension conjecture. Th…

Let $S_{\varepsilon}$ be the random-walk Metropolis process with position and ridge coordinates $(X_{\varepsilon,j},U_{\varepsilon,j})$, let $\widetilde{S}_{\varepsilon}$ be the sp…

Generalized diffusion-limit conjecture. As $n\to\infty$,

Let $Y_t$ denote the limiting fluctuation process, let $u_d(t,d-Y_t)$ be the relevant value-function derivative, let $F_{p,d}$ be the demand-batch-size-dependent function appearing…