Coupling, stationarity, and regeneration

By Hermann Thorisson. 2000

649 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications, Signal Processing

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Citations in the corpus

Advanced Probabilistic Couplings for Differential Privacy (2016, neutral): “This result is very much in the spirit of the optimal or maximal coupling for exact probabilistic couplings (see, e.g., [49]).”
Proving Differential Privacy via Probabilistic Couplings (2016, neutral): “Seeking to explain the power of liftings, Barthe et al. [6] establish a tight connection between probabilistic liftings and probabilistic couplings , a basic tool in probability theory [24, 30].”
Quantitative bounds on convergence of time-inhomogeneous Markov chains (2004, positive): “Using (5), the classical coupling inequality [see, e.g., Thorisson (2000), Chapter 2, Section 3] implies that |ξPnφ− ξ′Pnφ|= |Eξ⊗ξ′⊗δ0{φ(Xn)− φ(X ′ n)}| = |Eξ⊗ξ′⊗δ0{(φ(Xn)− φ(X ′ n))1(dn = 0)}| ≤ ( sup x∈X |φ(x)|/f(x) ) Eξ⊗ξ′⊗δ0{(f(Xn) + f(X ′ n))1(dn = 0)}.”
Invariant transports of stationary random measures and mass-stationarity (2009, methodology): “5 is negative, we might (as is the key idea in [27] and [28]) attempt to introduce a stationary independent background:”
The Markov chain Monte Carlo revolution (2008, background): “Book-length treatments of coupling are [61] and [86].”
Unbiased Markov chain Monte Carlo methods with couplings (2020, methodology): “How to sample from maximal couplings of continuous distributions is described in Thorisson (2000) and in Section 4.”
Size bias for one and all (2013, background): “The standard rigorous analysis of the waiting time paradox, for instance in [88], is a bit less direct, based on randomizing the starting point of the arrivals, so that the arrival times form a stationary sequence.”
Lectures on the Poisson Process (2017, background): “Thorisson [156] proved the existence of such couplings in a general group setting; see [157] for a discussion and more references.”
Novel scaling limits for critical inhomogeneous random graphs (2009, background): “67), the density of E q converges pointwise to that of Eq , which, by [32], (7.”
Probability on Trees and Networks (2017, background): “For more on coupling and shift coupling, see Thorisson (2000).”
General state space Markov chains and MCMC algorithms (2004, neutral): “A Markov chain with stationary distribution π(·) is uniformly ergodic if and only if supx∈X ‖Pn(x, ·)− π(·)‖ 1/2 for some n ∈ N. Proof.”
Universality for first passage percolation on sparse random graphs (2012, background): “where dTV denotes the total variation distance; see, for instance, [40], Theorem 6.”
Learning with Similarity Functions on Graphs using Matchings of Geometric Embeddings (2015, background): “…setting, the connection also opens up the opportunity to draw upon the theory and methods of optimal transport, including optimal couplings [38, 27] to prove rigorous results, in particular to verify the properties of a “good” similarity measure – which, as noted above, can often be quite…”