相关论文: Cutoff for the bidirectional East Process

We consider the classic problem of scheduling jobs with precedence constraints on a set of identical machines to minimize the makespan objective function. Understanding the exact approximability of the problem when the number of machines is…

In this paper, we study the biased random transposition shuffle, a natural generalization of the classical random transposition shuffle studied by Diaconis and Shahshahani. We diagonalize the transition matrix of the shuffle and use these…

We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…

Several two-boundary problems are solved for a special L\'{e}vy process: the Poisson process with an exponential component. The jumps of this process are controlled by a homogeneous Poisson process, the positive jump size distribution is…

This paper explores the mixing time of the random transposition walk on permutations with one-sided interval restrictions. In particular, we're interested in the notion of cutoff, a phenomenon which occurs when mixing occurs in a window of…

The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts…

In the present paper, we consider a class of Markov processes on the discrete circle which has been introduced by K\"onig, O'Connell and Roch. These processes describe movements of exchangeable interacting particles and are discrete…

We survey recent results concerning the total-variation mixing time of the simple exclusion process on the segment (symmetric and asymmetric) and a continuum analog, the simple random walk on the simplex with an emphasis on cutoff results.…

Circuit cutting partitions a large quantum circuit into smaller subcircuits that can be executed independently and recombined by classical post-processing. In classical state-vector simulation with full-state reconstruction, the runtime is…

We study the random walk on a finite dihedral group $G$ driven by the uniform measure on $k$ independently and uniformly chosen elements. We show that the walk exhibits cutoff with high probability throughout nearly the entire regime $1 \ll…

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…

Real-time data processing is a central aspect of particle physics experiments with high requirements on computing resources. The LHCb experiment must cope with the 30 million proton-proton bunches collision per second rate of the Large…

In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to…

We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…

We consider the Random-Cluster model on $(\mathbb{Z}/n\mathbb{Z})^d$ with parameters $p \in (0,1)$ and $q\ge 1$. This is a generalization of the standard bond percolation (with open probability $p$) which is biased by a factor $q$ raised to…

As semiconductor devices continue to scale down, process vari- ations become more relevant for circuit design. Facing such variations, statistical static timing analysis is introduced to model variations more accurately so that the…

We consider the Metropolis biased card shuffling (also called the multi-species ASEP on a finite interval or the random Metropolis scan). Its convergence to stationary was believed to exhibit a total-variation cutoff, and that was proved a…

We study a $d$-dimensional random walk with exponentially distributed increments conditioned so that the components stay ordered (in the sense of Doob). We find explicitly a positive harmonic function $h$ for the killed process and then…

We consider the production of a colourless system at next-to-leading order in the strong coupling constant $\alpha_s$. We impose a transverse-momentum cutoff, qtcut, on the colourless final state and we compute the power corrections for the…

We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point x\inH, the hyperplane through Tx whose normal…