Prokhorov — Convergence of random processes and limit
McKean-Vlasov limit for interacting random processes in random media
... Keyword., and phmses: Interacting particle systems; random media; McKean-Vlasov equation; large deviations; central limit theorem.. AMS 1991 subject classifications.[r] ...
39
Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology
... Gromov-Prokhorov convergence and use it to give a criterion for GHPU convergence which will be used for the proof of our scaling limit results in ...
48
Limit theorems for decomposable branching processes in a random environment
... branching processes in random environment we consider here can be viewed as a discrete-time stochastic model for the sizes of a geographically struc- tured population occupying islands labelled 0, 1, ...
21
On the rate of convergence in limit theorems for random sums via Trotter distance
... It is worth pointing out that the mathematical tools have been used in the study of limit theorems for random sums review to date, including characteristic function, positive lin- ear operators and ...
12
Convergence of Random Graphs
... The major result we present, from papers of Le Galle and Miermont, is that scale limit of certain classes of planar maps is the Brownian Map. The work is divided in three sections. In the first section we ...
62
Scaled Limit and Rate of Convergence for the Largest Eigenvalue from the Generalized Cauchy Random Matrix Ensemble
... Joseph Najnudel · Ashkan Nikeghbali · Felix Rubin Received: 24 June 2009 / Accepted: 22 October 2009 / Published online: 3 November 2009 © Springer Science+Business Media, LLC 2009 Abstract In this paper, we are ...
34
Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble
... ℜs 2 N 2ℜs + N 2ℜs + 1 , C(x) = 2ℜs + 1. Note that this only makes sense if ℜs 6= 0. One can then show that for t ∈ R, and ℜ(s) > 1/2, the equation (2.1) holds. In the case of s ∈ (1/2, ∞) ⊂ R, this Theorem was ...
34
Surjective Lévy-Prokhorov Isometries
... Yu.V. Prokhorov, the gen- eral theory of stochastic processes can be regarded as the theory of probability measures in complete separable metric ...stochastic processes de- pending upon a continuous ...
19
ON CONVERGENCE OF STOCHASTIC PROCESSES
... We turn next to conditions ensuring that a family of measures on Lip« is precompact. The basic fact here is a theorem due to Prokhorov [5 ] relating precompactness of measures on a space to compactness of sets in ...
6
Convergence determining classes in the central limit theorem
... 6 1. I n t r o d u c t i o n 1.1. R a t e s o f C o n v e r g e n c e in t h e C e n t r a l L i m i t T h e o r e m . The Central Limit Theorem asserts that a suitably normed sum of random variables ...
165
Local limit theorems and mod-phi convergence
... Local limit theorems and mod-phi convergence Dal Borgo, Martina ; Méliot, Pierre-Loïc ; Nikeghbali, Ashkan Abstract: We prove local limit theorems for mod- convergent sequences of random ...
38
On rate of convergence in non-central limit theorems
... of convergence in the central limit theorem using the Stein-Malliavin approach was ...stochastic processes was ...of convergence for Wasserstein topology was found and an upper bound for the ...
30
Local convergence of random graph colorings
... We omit the subscript G and/or k where it is apparent from the context. Thus, the symbol h · i G,k refers to the average over randomly chosen k- colorings of a fixed graph G. By contrast, the standard notation E [· ], P ...
41
The Complete Convergence of Exchangeable Random Variables
... Probability limit theory is one of the branches of probability and also is important basic theory of the science of probability and ...statistics. Limit theory mainly study independent random ...
5
Limit theorems for one and two-dimensional random walks in random scenery
... functional limit theorem has been established in [11] and a local limit theorem in ...the convergence of the finite-dimensional distributions and a local limit theorem when α = d ...functional ...
18
Limit theorems for a random directed slab graph
... of vertices. As a matter of fact, in [18], the random graph was a special case of a more general dynamical system (the “infinite bin model”) with stationary and ergodic input. In this paper, we follow a different ...
26
Scaling limit of critical systems in random geometry
... Outline. The structure of the paper is as follows. In Section 5.2, we discuss briefly the necessary background theory, and collect some results that will be important to us. We also define the class of SLE κ (ρ) process ...
219
Central Limit Theorems for Empirical Processes Based on Stochastic Processes
... (weak convergence to a Gaussian limit), “a limit” has to ...Gaussian processes under assumptions (like L-condition, WL-condition or “ν n,t ...
97
Branching processes in random environment
... thesis, limit theorems describing intermediately subcritical BPREs have been ...associated random walk is in a strict descending ladder point) as well as finding a proof for the conditional limit ...
120
Scaling limit for the random walk on the largest connected component of the critical random graph
... Although we will not apply it in its following form, for completeness, it seems appro- priate to put all the above pieces together and state a (simplified version of) the main result of [1], which demonstrates the ...
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