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作者：Chapon, Francois; Chhaibi, Reda
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：The classical theorem by Pitman states that a Brownianmotionminus twice its running infimum enjoys the Markov property. On the one hand, Biane understood that Pitman's theorem is intimately related to the representation theory of the quantum group U-q (sl(2)), in the so-called crystal regime q -> 0. On the other hand, Bougerol and Jeulin showed the appearance of exactly the same Pitman transform in the infinite curvature limit r. 8 of a Brownian motion on the hyperbolic space H-3 = SL2(C)/SU2....
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作者：Neuman, Eyal; Zheng, Xinghua
作者单位：Imperial College London; Hong Kong University of Science & Technology
摘要：We consider a branching random walk on Z started by n particles at the origin, where each particle disperses according to a mean-zero random walk with bounded support and reproduces with mean number of offspring 1 + theta/n. For t >= 0, we study M-nt, the rightmost position reached by the branching random walk up to generation [nt]. Under certain moment assumptions on the branching law, we prove that M-nt/root n converges weakly to the rightmost support point of the local time of the limiting ...
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作者：Buchholz, Simon
作者单位：University of Bonn
摘要：We consider gradient fields on Z(d) for potentials V that can be expressed as e(-V(x)) = pe -qx(2)/2 + (1 - p)e-x(2)/2. This representation allows us to associate a random conductance type model to the gradient fields with zero tilt. We investigate this random conductance model and prove correlation inequalities, duality properties, and uniqueness of the Gibbs measure in certain regimes. We then show that there is a close relation between Gibbs measures of the random conductance model and grad...
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作者：[Anonymous]
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作者：O'Connell, Neil
作者单位：University College Dublin
摘要：We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related to K-Bessel functions of matrix argument and multivariate generalisations of these functions. The latter are eigenfunctions of a particular quantisation of the non-Abelian Toda lattice.
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作者：Michaeli, Peleg; Nachmias, Asaf; Shalev, Matan
作者单位：Tel Aviv University
摘要：We show that the diameter of a uniformly drawn spanning tree of a connected graph on n vertices which satisfies certain high-dimensionality conditions typically grows like Theta(root n). In particular this result applies to expanders, finite tori Z(m)(d) of dimension d >= 5, the hypercube {0, 1}(m), and small perturbations thereof.
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作者：Ding, Jian; Gwynne, Ewain; Sepulveda, Avelio
作者单位：University of Pennsylvania; University of Chicago; Universidad de Chile
摘要：Discrete Liouville first passage percolation (LFPP) with parameter xi > 0 is the random metric on a sub-graph of Z(2) obtained by assigning each vertex z a weight of e(xi h(z)), where h is the discrete Gaussian free field. We show that the distance exponent for discrete LFPP is strictly positive for all xi > 0. More precisely, the discrete LFPP distance between the inner and outer boundaries of a discrete annulus of size 2(n) is typically at least 2(alpha n) for an exponent alpha > 0 depending...
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作者：Gassiat, Paul; Oberhauser, Harald; Zou, Christina Z.
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Oxford
摘要：We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of space-time subsets, so-called Root barriers. Our main result is, besides the existence and optimality, a potential-theoretic characterisation of this Root barrier as a free boundary. If the generator of the Markov process is sufficiently regular, this reduces to a...
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作者：Kim, Seonwoo
作者单位：Seoul National University (SNU)
摘要：We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by Bianchi et al. (Electron J Probab 22:1-34, 2017), which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that N/d(N)(2) is indeed the correct second time scale for the most general class of reversible inclusion processes, and thus prove the first conjecture of the foresaid study. Here, N denotes the numbe...
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作者：Dabrock, Nils; Hofmanova, Martina; Roger, Matthias
作者单位：Dortmund University of Technology; University of Bielefeld
摘要：We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. For the first time, we are able to construct martingale solutions which satisfy the equation pointwise and not only in a generalized (distributional or viscosity) sense. Moreover, we study their large-time behavior. Our analysis is based on a viscous approximation and new global bounds, namely, an L-w,x,t(infinity) estimate for the gradient and an L-w, x,t(2) bound for the Hessian. T...
