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作者：Bhamidi, Shankar; Dhara, Souvik; van der Hofstad, Remco
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Purdue University System; Purdue University; Eindhoven University of Technology
摘要：We study the critical behavior for percolation on inhomogeneous random networks on n vertices, where the weights of the vertices follow a power-law distribution with exponent tau is an element of (2, 3). Such networks, often referred to as scale-free networks, exhibit critical behavior when the percolation probability tends to zero at an appropriate rate, as n -> infinity. We identify the critical window for several scale-free random graph models, such as the Norros-Reittu model, Chung-Lu mode...
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作者：Chatzigeorgiou, Georgiana; Morfe, Peter; Otto, Felix; Wang, Lihan
作者单位：Max Planck Society
摘要：We analyze the large-time asymptotics of a passive tracer with drift equal to the curl of the Gaussian free field in two dimensions with ultra-violet cutoff at scale unity. We prove that the mean-squared displacement scales like t root lnt, as predicted in the physics literature. This improves the asymptotics recently established in recent work of Cannizzaro, Haunschmidt-Sibitz, and Toninelli (Ann. Probab. 50 (2022) 2475-2498), which uses mathematical-physics type analysis in Fock space. Our a...
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作者：Chen, Zhen-Qing; Wang, Jie-Ming
作者单位：University of Washington; University of Washington Seattle; Beijing Institute of Technology; Beijing Institute of Technology
摘要：In this paper a necessary and sufficient condition is obtained for the scale invariant boundary Harnack principle (BHP in abbreviation) for a large class of Hunt processes on metric measure spaces that are in weak duality with another Hunt process. We then apply it to a class of discontinuous subordinate Brownian motions with Gaussian components in Wdfor which the L & eacute;vy density of the subordinators satisfies some mild comparability condition. We show that the scale invariant BHP holds ...
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作者：Schertzer, Emmanuel; Tourniaire, Julie
作者单位：University of Vienna; Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift-mu and killed upon reaching 0. More precisely, the particles branch at rate r(x) = (1 + W (x))/2, where W is a compactly supported and nonnegative smooth function and the drift mu is chosen in such a way that the system is critical in some sense. This particle system can be seen as an analytically tractable model for fluctuating fronts, describing ...
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作者：Li, Jhih-huang; Saenz, Axel
作者单位：National Taiwan University; Oregon State University
摘要：We give contour integral formulas for the generating function of the joint distribution of the PushASEP on a ring. We obtained these formulas through a rigorous treatment of Bethe ansatz. The approach relies on residue computations and controlling the location of the Bethe roots, which we achieve by partially decoupling the Bethe equations and extending the system of equations. Moreover, we are able to use our formulas to compute the asymptotic fluctuations for the flat and step initial condit...
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作者：Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W.
作者单位：University of Bonn; University of Bonn; University of Munich; Technical University of Munich
摘要：We show that the vertex-reinforced jump process on the d-dimensional lattice with long-range jumps is transient in any dimension d as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis of the corresponding random environment on finite boxes, a comparison with a hierarchical model, and the reduction of the hierarchical model to a nonhomogeneous effective one-dimensional model. For d >= 3 we also prove transience of the vertex-reinforced jump pr...
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作者：Heilman, Steven
作者单位：University of Southern California
摘要：We prove a vector-valued inequality for the Gaussian noise stability (i.e. we prove a vector-valued Borell inequality) for Euclidean functions taking values in the two-dimensional sphere, for all correlation parameters at most 1/10 in absolute value. This inequality was conjectured (for all correlation son and Wright. Such an inequality is needed to prove sharp computational hardness of the product state Quantum MAX-CUT problem, assuming the unique games conjecture. In fact, assuming the uniqu...
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作者：Jorritsma, Joost; Komjathy, Julia; Mitsche, Dieter
作者单位：University of Oxford; Delft University of Technology; Pontificia Universidad Catolica de Chile; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assume that the model is supercritical: there is an infinite component. We identify the stretch-exponent zeta is an element of (0, 1) of the decay of the cluster-size distribution. That is, with |C(0)| denoting the number of vertices in the component of the vertex at 0 is an element of R-d, we prove P...
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作者：Das, Sayan; Liao, Yuchen; Mucciconi, Matteo
作者单位：Columbia University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore
摘要：In this paper we study large time large deviations for the height function h(x, t) of the q-deformed polynuclear growth introduced in (Int. Math. Res. Not. IMRN 7 (2023) 5728-5780). We show that the upper-tail deviations have speed t and derive an explicit formula for the rate function Phi+(mu). On the other hand, we show that the lower-tail deviations have speed t2 and express the corresponding rate function Phi-(mu) in terms of a variational problem. Our analysis relies on distributional ide...
