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When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal H\"older exponent obtainable under reparametrization. In this paper, we show that…

We prove the existence and uniqueness of multiple SLE$_\kappa$ associated with any given link pattern for $\kappa\in (4,6]$. We also have the uniqueness for $\kappa\in (6,8)$. The multiple SLE$_\kappa$ law is constructed by first…

We consider the Schramm-Loewner evolution (SLE$_\kappa$) for $\kappa \in (4,8)$, which is the regime where the curve is self-intersecting but not space-filling. We show that there exists $\delta_0>0$ such that for $\kappa \in (8 -…

Determining the number of stable phase-locked solutions for locally coupled Kuramoto models is a long-standing mathematical problem with important implications in biology, condensed matter physics and electrical engineering among others. We…

We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called $\textit{cusp times}$ $t_i^2 = g^2 \log x_{i-1,i}^2\log x_{i,i+1}^2$ are held fixed and the t'Hooft…

The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary…

We have numerically studied the properties of the interface induced in the ferromagnetic random-bond three-state Potts model by symmetry-breaking boundary conditions. The fractal dimension $d_f$ of the interface was determined. The…

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails…

We compute the almost-sure Hausdorff dimension of the double points of chordal SLE_kappa for kappa > 4, confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of…

We compute the entropy of entanglement between the first $N$ spins and the rest of the system in the ground states of a general class of quantum spin-chains. We show that under certain conditions the entropy can be expressed in terms of…

We study the binary symmetric perceptron model, and in particular its atypical solutions. While the solution-space of this problem is dominated by isolated configurations, it is also solvable for a certain range of constraint density…

We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…

Duminil-Copin and Manolescu (2022) recently proved the scaling relations for planar Fortuin-Kasteleyn (FK) percolation. In particular, they showed that the one-arm exponent and the mixing rate exponent are sufficient to derive the other…

We consider the correlation function of a circular Wilson loop with two local scalar operators at generic 4-positions in planar N=4 supersymmetric gauge theory. We show that such correlator is fixed by conformal invariance up to a function…

We prove upper bounds for the probability that a radial SLE$_{\kappa}$ curve, $\kappa\in(0,8)$, comes within specified radii of $n$ different points in the unit disc. Using this estimate, we then prove a similar upper bound for a…

The connectivity is an important parameter to evaluate the robustness of a network. As a generalization, structure connectivity and substructure connectivity of graphs were proposed. For connected graphs $G$ and $H$, the $H$-structure…

Let $G$ be a finite group, and let $\kappa(G)$ be the probability that elements $g$, $h\in G$ are conjugate, when $g$ and $h$ are chosen independently and uniformly at random. The paper classifies those groups $G$ such that $\kappa(G) \geq…

We propose to probe the electroweak symmetry breaking sector by measuring the effective couplings of the top quark to gauge bosons. Using precision LEP data, we constrain the non--universal couplings of t-t-Z and t-b-W, parameterized by…

We consider the Constrained-degree percolation model in random environment on the square lattice. In this model, each vertex $v$ has an independent random constraint ${\kappa}_v$ which takes the value $j\in \{0,1,2,3\}$ with probability…

We define the correlation of holes on the triangular lattice under periodic boundary conditions and study its asymptotics as the distances between the holes grow to infinity. We prove that the joint correlation of an arbitrary collection of…