Related papers: The $L^2$-cutoffs for reversible Markov chains
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
This paper generalizes the work of Kendall [Electron. Comm. Probab. 9 (2004) 140--151], which showed that perfect simulation, in the form of dominated coupling from the past, is always possible (although not necessarily practical) for…
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…
We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…
We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance…
We propose a distance between continuous-time Markov chains (CTMCs) and study the problem of computing it by comparing three different algorithmic methodologies: iterative, linear program, and on-the-fly. In a work presented at FoSSaCS'12,…
We consider the class of (possibly killed) spectrally positive L\'evy process that have been time-changed by the inverse of an integral functional. Within this class we characterize the family of those processes which satisfy the following…
The non-linear corrections (NLC) to the longitudinal structure function in a limited approach is derived at low values of the Bjorken variable $x$ by using the Laplace transforms technique. The non-linear behavior of the longitudinal…
This paper features a Cram\'er's theorem for finite-state Markov chains indexed by rooted $d$-trees, obtained via the method of types in the classical analysis of large deviations. Along with the theorem comes two applications: an…
This paper considers the $(n,k)$-Bernoulli--Laplace model in the case when there are two urns, the total number of red and white balls is the same, and the number of selections $k$ at each step is on the same asymptotic order as the number…
We consider an irreducible continuous time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for…
The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
We propose some backward-forward martingale decompositions for functions of reversible Markov chains. These decompositions are used to prove the functional CLT for reversible Markov chains with asymptotically linear variance of partial…
Exactly solvable (spinless) lattice fermions with wide range interactions are constructed explicitly based on {\em exactly solvable stationary and reversible Markov chains} $\mathcal{K}^R$ reported a few years earlier by Odake and myself.…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
Bhattacharya et al. (2015, Journal of the American Statistical Association 110(512): 1479-1490) introduce a novel prior, the Dirichlet-Laplace (DL) prior, and propose a Markov chain Monte Carlo (MCMC) method to simulate posterior draws…