47 citations · 297 across the 23 of their papers we have counts for
23 papers
Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes
Tobias Johnson, Erol Peköz
Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Peköz, Röllin, and Ross (2016, arXiv:1309.4183 [mat…
Diffusion-limited annihilating systems and the increasing convex order
Riti Bahl, Philip Barnet, Tobias Johnson +1
We consider diffusion-limited annihilating systems with mobile -particles and stationary -particles placed throughout a graph. Mutual annihilation occurs whenever an -part…
Continuous phase transitions on Galton-Watson trees
Tobias Johnson
Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galto…
Particle density in diffusion-limited annihilating systems
Tobias Johnson, Matthew Junge, Hanbaek Lyu +1
Place an -particle at each site of a graph independently with probability and otherwise place a -particle. - and -particles perform independent continuous time rand…
Sensitivity of the frog model to initial conditions
Tobias Johnson, Leonardo T. Rolla
The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an act…
Random tree recursions: which fixed points correspond to tangible sets of trees?
Tobias Johnson, Moumanti Podder, Fiona Skerman
Let be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only i…
Cover time for the frog model on trees
Christopher Hoffman, Tobias Johnson, Matthew Junge
The frog model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of on the full -ary tree of heig…
Infection spread for the frog model on trees
Christopher Hoffman, Tobias Johnson, Matthew Junge
The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted -ary tree with particle…
The critical density for the frog model is the degree of the tree
Tobias Johnson, Matthew Junge
The frog model on the rooted d-ary tree changes from transient to recurrent as the number of frogs per site is increased. We prove that the location of this transition is on the sa…
Local limit of the fixed point forest
Tobias Johnson, Anne Schilling, Erik Slivken
Consider the following partial "sorting algorithm" on permutations: take the first entry of the permutation in one-line notation and insert it into the position of its own value. C…
Stochastic orders and the frog model
Tobias Johnson, Matthew Junge
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths…
Bounds to the normal for proximity region graphs
Larry Goldstein, Tobias Johnson, Raphaël Lachièze-Rey
In a proximity region graph in , two distinct points of a point process are connected when the 'forbidden region' these points determine…
Size biased couplings and the spectral gap for random regular graphs
Nicholas A. Cook, Larry Goldstein, Tobias Johnson
Let be the second largest eigenvalue in absolute value of a uniform random -regular graph on vertices. It was famously conjectured by Alon and proved by Friedman that if…
From transience to recurrence with Poisson tree frogs
Christopher Hoffman, Tobias Johnson, Matthew Junge
Consider the following interacting particle system on the -ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are…
Eigenvalue fluctuations for random regular graphs
Tobias Johnson
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of un…
Recurrence and transience for the frog model on trees
Christopher Hoffman, Tobias Johnson, Matthew Junge
The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the in…
Quantitative Small Subgraph Conditioning
Tobias Johnson, Elliot Paquette
We revisit the method of small subgraph conditioning, used to establish that random regular graphs are Hamiltonian a.a.s. We refine this method using new technical machinery for ra…
The Marčenko-Pastur law for sparse random bipartite biregular graphs
Ioana Dumitriu, Tobias Johnson
We prove that the empirical spectral distribution of a (d_L, d_R)-biregular, bipartite random graph, under certain conditions, converges to a symmetrization of the Marčenko-Pastur…
Cycles and eigenvalues of sequentially growing random regular graphs
Tobias Johnson, Soumik Pal
Consider the sum of many i.i.d. random permutation matrices on labels along with their transposes. The resulting matrix is the adjacency matrix of a random regular (multi)-…
Exchangeable pairs, switchings, and random regular graphs
Tobias Johnson
We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cy…
Functional limit theorems for random regular graphs
Ioana Dumitriu, Tobias Johnson, Soumik Pal +1
Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix o…
On Universal Cycles for Multisets
Glenn Hurlbert, Tobias Johnson, Joshua Zahl
A Universal Cycle for t-multisets of [n]={1,...,n} is a cyclic sequence of integers from [n] with the property that each t-multiset of [n] appears exactly once c…
Universal Cycles on 3-Multisets
Tobias L. Johnson, Joshua Zahl
Consider the collection of all t-multisets of {1,...,n}. A universal cycle on multisets is a string of numbers, each of which is between 1 and n, such that if these numbers are con…