Related papers: Conformal Loop Ensembles: The Markovian characteri…

We give a Markov chain based perfect sampler for uniform sampling solutions of constraint satisfaction problems (CSP). Under some mild Lov\'asz local lemma conditions where each constraint of the CSP has a small number of forbidden local…

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…

The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…

We construct loop soups for general Markov processes without transition densities and show that the associated permanental process is equal in distribution to the loop soup local time. This is used to establish isomorphism theorems…

This paper initiates the study of the conformal field theory of the SLE$_\kappa$ loop measure $\nu$ for $\kappa\in(0,4]$, the range where the loop is almost surely simple. First, we construct two commuting representations…

We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and…

We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…

For each $\alpha \in \mathbb{R}$, $t \geq 1$, we show that there exists a unique $\mathbb{N}$-indexed line ensemble of random continuous curves $\mathbb{R}_{\le 0} \to \mathbb{R}$ with the following properties: (1) The top curve is…

Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes, for instance, groups and commutative Moufang loops. We study uniquely 2-divisible automorphic loops, particularly automorphic loops…

In this article, we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow the recently developed system level synthesis (SLS) approach and impose locality structure on the resulting…

We address the scaling limits of random curves arising from, e.g., planar lattice models, especially in rough domains. The well-known precompactness conditions of Kemppainen and Smirnov show that certain crossing probability estimates…

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…

Consider a sequence of Poisson point processes of non-trivial loops with certain intensity measures $(\mu^{(n)})_n$, where each $\mu^{(n)}$ is explicitly determined by transition probabilities $p^{(n)}$ of a random walk on a finite state…

The Super Learner (SL) is a widely used ensemble method that combines predictions from a library of learners based on their predictive performance. Interval predictions are of considerable practical interest because they allow uncertainty…

In this work, we investigate a novel setting of Markovian loop measures and introduce a new class of loop measures called Bosonic loop measures. Namely, we consider loop soups with varying intensity $ \mu\le 0 $ (chemical potential in…

This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual systems in the ensemble are sparse and governed by the same sparsity pattern, and undergo switching among…

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal…

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All…

We construct the canonical Brownian motion on the gasket of conformal loop ensembles (CLE$_\kappa$) for $\kappa \in (4,8)$ (which is the range of parameter values in which loops of the CLE$_\kappa$ can intersect themselves, each other, and…

Based on discrete observations $X_0,X_{\Delta},\dots, X_{n\Delta}$ for $\Delta=n^{-\gamma}$ with $\gamma\in [0,1)$ of the null-recurrent dynamic $dX_t = \sigma(X_t)dW_t$ with a Brownian motion $W$ and $\sigma(x)=\alpha\mathbb{1}\{x<\rho\} +…