59 citations · 216 across the 22 of their papers we have counts for
24 papers
Sharp detection thresholds for random geometric graphs with polynomial average degrees
Hang Du, Cheng Mao, Nike Sun +2
We study the random geometric graph formed by connecting independent uniform points on whenever their inner product exceeds a threshold chosen to give edge de…
Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the Regime
Hang Du, Cheng Mao, Nike Sun +2
A random geometric graph (RGG) is generated by first sampling latent points independently and uniformly from the unit sphere in , and then connecting…
Sharp thresholds in inference of planted subgraphs
Elchanan Mossel, Jonathan Niles-Weed, Youngtak Sohn +2
A major question in the study of the Erdős--Rényi random graph is to understand the probability that it contains a given subgraph. This study originated in classical work of Erdős…
Locality of critical percolation on expanding graph sequences
Michael Ren, Nike Sun
We study the locality of critical percolation on finite graphs: let be a sequence of finite graphs, converging locally weakly to a (random, rooted) infinite graph . Consid…
A second moment proof of the spread lemma
Elchanan Mossel, Jonathan Niles-Weed, Nike Sun +1
This note concerns a well-known result which we term the ``spread lemma,'' which establishes the existence (with high probability) of a desired structure in a random set. The sprea…
On the Second Kahn--Kalai Conjecture
Elchanan Mossel, Jonathan Niles-Weed, Nike Sun +1
For any given graph , we are interested in , the minimal such that the Erdős-Rényi graph contains a copy of with probability at least .…
Sharp threshold sequence and universality for Ising perceptron models
Shuta Nakajima, Nike Sun
We study a family of Ising perceptron models with -valued activation functions. This includes the classical half-space models, as well as some of the symmetric models cons…
Gardner formula for Ising perceptron models at small densities
Erwin Bolthausen, Shuta Nakajima, Nike Sun +1
We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-s…
Breaking of 1RSB in random MAX-NAE-SAT
Zsolt Bartha, Nike Sun, Yumeng Zhang
For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. For random -SAT a…
Capacity lower bound for the Ising perceptron
Jian Ding, Nike Sun
We consider the Ising perceptron with gaussian disorder, which is equivalent to the discrete cube intersected by random half-spaces. The perceptron's capacity is…
Spectral algorithms for tensor completion
Andrea Montanari, Nike Sun
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed…
The number of solutions for random regular NAE-SAT
Allan Sly, Nike Sun, Yumeng Zhang
Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfi…
Shotgun assembly of random regular graphs
Brice Huang, Elchanan Mossel, Nike Sun +2
Mossel and Ross (2019) introduce the shotgun assembly problem for random graphs: what radius ensures that the random graph can be uniquely recovered from its list of rooted…
Supercritical minimum mean-weight cycles
Jian Ding, Nike Sun, David B. Wilson
We study the weight and length of the minimum mean-weight cycle in the stochastic mean-field distance model, i.e., in the complete graph on vertices with edges weighted by inde…
Proof of the satisfiability conjecture for large k
Jian Ding, Allan Sly, Nike Sun
We establish the satisfiability threshold for random -SAT for all , with an absolute constant. That is, there exists a limiting density such that a rand…
Maximum independent sets on random regular graphs
Jian Ding, Allan Sly, Nike Sun
We determine the asymptotics of the independence number of the random -regular graph for all . It is highly concentrated, with constant-order fluctuations around $nα_…
Satisfiability threshold for random regular NAE-SAT
Jian Ding, Allan Sly, Nike Sun
We consider the random regular -NAE-SAT problem with variables each appearing in exactly clauses. For all exceeding an absolute constant , we establish explicit…
On the asymptotics of dimers on tori
Richard W. Kenyon, Nike Sun, David B. Wilson
We study asymptotics of the dimer model on large toric graphs. Let be a weighted -periodic planar graph, and let be a large-index sublatt…
The Hausdorff dimension of the CLE gasket
Jason Miller, Nike Sun, David B. Wilson
The conformal loop ensemble is the canonical conformally invariant probability measure on noncrossing loops in a proper simply connected domain in the complex plan…
The computational hardness of counting in two-spin models on d-regular graphs
Allan Sly, Nike Sun
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (…
Factor models on locally tree-like graphs
Amir Dembo, Andrea Montanari, Nike Sun
We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree , and study the existence of the free energy density $…
Central limit theorem for biased random walk on multi-type Galton-Watson trees
Amir Dembo, Nike Sun
Let T be a rooted supercritical multi-type Galton-Watson (MGW) tree with types coming from a finite alphabet, conditioned to non-extinction. The lambda-biased random walk (X_t, t>=…
Strong path convergence from Loewner driving function convergence
Scott Sheffield, Nike Sun
We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We e…
Conformally invariant scaling limits in planar critical percolation
Nike Sun
This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on t…