Wai-Kit Lam

activity

20152026

most citedEstimates for the empirical distribution along a geodesic in first-passage percolation

5 citations · 9 across the 13 of their papers we have counts for

collaborators

16 papers

math.PR2026

Central Limit Theorem of Maximum Weight Matching on Random Graphs with Prescribed Degrees

Shichen Jing, Wai-Kit Lam, Arnab Sen

We prove an annealed central limit theorem for the weight of the maximum weight matching on uniformly random simple graphs with prescribed, uniformly bounded degrees and i.i.d. exp…

math.PR2025

Correlation Decay for Maximum Weight Matchings on Sparse Graphs

Wai-Kit Lam, Arnab Sen

We study correlation decay for the maximum weight matching problem on sparse graphs with i.i.d. edge weights. We show exponential decay of correlations when the underlying graphs a…

math.PR2025

Asymptotics for first-passage percolation on logarithmic subgraphs of $Z^{2}$

Michael Damron, Wai-Kit Lam

For $a > 0$ and $b \geq 0$ , let $G_{a, b}$ be the subgraph of $Z^{2}$ induced by the vertices between the first coordinate axis and the graph of the function $f = f_{a…

math.PR2025

Moderate deviations in first-passage percolation for bounded weights

Wai-Kit Lam, Shuta Nakajima

We investigate the moderate and large deviations in first-passage percolation (FPP) with bounded weights on $Z^{d}$ for $d \geq 2$ . Write $T (x, y)$ for the…

math.PR2023

Exceptional behavior in critical first-passage percolation and random sums

Michael Damron, Jack Hanson, David Harper +1

We study first-passage percolation (FPP) on the square lattice. The model is defined using i.i.d. nonnegative random edge-weights $(t_{e})$ associated to the nearest neighbor edges o…

math.PR2023

Universality of Superconcentration in the Sherrington-Kirkpatrick Model

Wei-Kuo Chen, Wai-Kit Lam

We study the universality of superconcentration for the free energy in the Sherrington-Kirkpatrick (SK) model. In arXiv:0907.3381, Chatterjee showed that when the system consists o…

math.PR2022★ 1 cited

Central Limit Theorem in Disordered Monomer-Dimer Model

Wai-Kit Lam, Arnab Sen

We consider the disordered monomer-dimer model on general finite graphs with bounded degrees. Under the finite fourth moment assumption on the weight distributions, we prove a Gaus…

math.PR2022

On the number and size of holes in the growing ball of first-passage percolation

Michael Damron, Julian Gold, Wai-Kit Lam +1

First-passage percolation is a random growth model defined on $Z^{d}$ using i.i.d. nonnegative weights $(τ_{e})$ on the edges. Letting $T (x, y)$ be the distance between vertice…

math.PR2021

Transitions for exceptional times in dynamical first-passage percolation

Michael Damron, Jack Hanson, David Harper +1

In first-passage percolation (FPP), we let $(τ_{v})$ be i.i.d. nonnegative weights on the vertices of a graph and study the weight of the minimal path between distant vertices. If $F…

math.PR2021

Near-critical avalanches in 2D frozen percolation and forest fires

Wai-Kit Lam, Pierre Nolin

We study two closely related processes on the triangular lattice: frozen percolation, where connected components of occupied vertices freeze (they stop growing) as soon as they con…

math.PR2020★ 5 cited

Estimates for the empirical distribution along a geodesic in first-passage percolation

Michael Damron, Jack Hanson, Christopher Janjigian +2

In first-passage percolation, we assign i.i.d.~nonnegative weights $(t_{e})$ to the nearest-neighbor edges of $Z^{d}$ and study the induced pseudometric $T = T (x, y)$ . In this…

math.PR2020

Universality of Approximate Message Passing Algorithms

Wei-Kuo Chen, Wai-Kit Lam

We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $n \times n$ random symmetric matrix $A$ . We…

math.PR2019

Universality of the time constant for $2 D$ critical first-passage percolation

Michael Damron, Jack Hanson, Wai-Kit Lam

We consider first-passage percolation (FPP) on the triangular lattice with vertex weights $(t_{v})$ whose common distribution function $F$ satisfies $F (0) = 1/2$ . This is known as the…

math.PR2019

Order of Fluctuations of the Free Energy in the SK Model at Critical Temperature

Wei-Kuo Chen, Wai-Kit Lam

We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature.…

math.PR2017

The size of the boundary in first-passage percolation

Michael Damron, Jack Hanson, Wai-Kit Lam

First-passage percolation is a random growth model defined using i.i.d. edge-weights $(t_{e})$ on the nearest-neighbor edges of $Z^{d}$ . An initial infection occupies the orig…

math.PR2015★ 3 cited

Asymptotics for $2 D$ Critical First Passage Percolation

Michael Damron, Wai-Kit Lam, Xuan Wang

We consider first-passage percolation on $Z^{2}$ with i.i.d. weights, whose distribution function satisfies $F (0) = p_{c} = 1/2$ . This is sometimes known as the "critical case…

Central Limit Theorem of Maximum Weight Matching on Random Graphs with Prescribed Degrees

Correlation Decay for Maximum Weight Matchings on Sparse Graphs

Asymptotics for first-passage percolation on logarithmic subgraphs of Z2

Moderate deviations in first-passage percolation for bounded weights

Exceptional behavior in critical first-passage percolation and random sums

Universality of Superconcentration in the Sherrington-Kirkpatrick Model

Central Limit Theorem in Disordered Monomer-Dimer Model

On the number and size of holes in the growing ball of first-passage percolation

Transitions for exceptional times in dynamical first-passage percolation

Near-critical avalanches in 2D frozen percolation and forest fires

Estimates for the empirical distribution along a geodesic in first-passage percolation

Universality of Approximate Message Passing Algorithms

Universality of the time constant for 2D critical first-passage percolation

Order of Fluctuations of the Free Energy in the SK Model at Critical Temperature

The size of the boundary in first-passage percolation

Asymptotics for 2D Critical First Passage Percolation

Asymptotics for first-passage percolation on logarithmic subgraphs of $Z^{2}$

Universality of the time constant for $2 D$ critical first-passage percolation

Asymptotics for $2 D$ Critical First Passage Percolation