Displaying similar documents to “Supercritical self-avoiding walks are space-filling”

Asymptotic behavior of a stochastic combustion growth process

Alejandro Ramírez, Vladas Sidoravicius (2004)

Journal of the European Mathematical Society

Similarity:

We study a continuous time growth process on the d -dimensional hypercubic lattice 𝒵 d , which admits a phenomenological interpretation as the combustion reaction A + B 2 A , where A represents heat particles and B inert particles. This process can be described as an interacting particle system in the following way: at time 0 a simple symmetric continuous time random walk of total jump rate one begins to move from the origin of the hypercubic lattice; then, as soon as any random walk visits a site...

Positivity of integrated random walks

Vladislav Vysotsky (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Take a centered random walk S n and consider the sequence of its partial sums A n : = i = 1 n S i . Suppose S 1 is in the domain of normal attraction of an α -stable law with 1 l t ; α 2 . Assuming that S 1 is either right-exponential (i.e. ( S 1 g t ; x | S 1 g t ; 0 ) = e - a x for some a g t ; 0 and all x g t ; 0 ) or right-continuous (skip free), we prove that { A 1 g t ; 0 , , A N g t ; 0 } C α N 1 / ( 2 α ) - 1 / 2 as N , where C α g t ; 0 depends on the distribution of the walk. We also consider a conditional version of this problem and study positivity of integrated discrete bridges.

Uniform mixing time for random walk on lamplighter graphs

Júlia Komjáthy, Jason Miller, Yuval Peres (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Suppose that 𝒢 is a finite, connected graph and X is a lazy random walk on 𝒢 . The lamplighter chain X associated with X is the random walk on the wreath product 𝒢 = 𝐙 2 𝒢 , the graph whose vertices consist of pairs ( f ̲ , x ) where f is a labeling of the vertices of 𝒢 by elements of 𝐙 2 = { 0 , 1 } and x is a vertex in 𝒢 . There is an edge between ( f ̲ , x ) and ( g ̲ , y ) in 𝒢 if and only if x is adjacent to y in 𝒢 and f z = g z for all z x , y . In each step, X moves from a configuration ( f ̲ , x ) by updating x to y using the transition rule of X and then...

Further generalized versions of Ilmanen’s lemma on insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2021)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The author proved in 2018 that if G is an open subset of a Hilbert space, f 1 , f 2 : G continuous functions and ω a nontrivial modulus such that f 1 f 2 , f 1 is locally semiconvex with modulus ω and f 2 is locally semiconcave with modulus ω , then there exists f C loc 1 , ω ( G ) such that f 1 f f 2 . This is a generalization of Ilmanen’s lemma (which deals with linear modulus and functions on an open subset of n ). Here we extend the mentioned result from Hilbert spaces to some superreflexive spaces, in particular to L p spaces, p [ 2 , ) . We...

A density version of the Carlson–Simpson theorem

Pandelis Dodos, Vassilis Kanellopoulos, Konstantinos Tyros (2014)

Journal of the European Mathematical Society

Similarity:

We prove a density version of the Carlson–Simpson Theorem. Specifically we show the following. For every integer k 2 and every set A of words over k satisfying lim sup n | A [ k ] n | / k n > 0 there exist a word c over k and a sequence ( w n ) of left variable words over k such that the set c { c w 0 ( a 0 ) . . . w n ( a n ) : n and a 0 , . . . , a n [ k ] } is contained in A . While the result is infinite-dimensional its proof is based on an appropriate finite and quantitative version, also obtained in the paper.

2-Cohomology of semi-simple simply connected group-schemes over curves defined over p -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let X be a proper, smooth, geometrically connected curve over a p -adic field k . Lichtenbaum proved that there exists a perfect duality: Br ( X ) × Pic ( X ) / between the Brauer and the Picard group of X , from which he deduced the existence of an injection of Br ( X ) in P X Br ( k P ) where P X and k P denotes the residual field of the point P . The aim of this paper is to prove that if G = G ˜ is an X e t - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results...

Giant component and vacant set for random walk on a discrete torus

Itai Benjamini, Alain-Sol Sznitman (2008)

Journal of the European Mathematical Society

Similarity:

We consider random walk on a discrete torus E of side-length N , in sufficiently high dimension d . We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time u N d . We show that when u is chosen small, as N tends to infinity, there is with overwhelming probability a unique connected component in the vacant set which contains segments of length const log N . Moreover, this connected component occupies a...

Size of the giant component in a random geometric graph

Ghurumuruhan Ganesan (2013)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

In this paper, we study the size of the giant component C G in the random geometric graph G = G ( n , r n , f ) of n nodes independently distributed each according to a certain density f ( · ) in [ 0 , 1 ] 2 satisfying inf x [ 0 , 1 ] 2 f ( x ) g t ; 0 . If c 1 n r n 2 c 2 log n n for some positive constants c 1 , c 2 and n r n 2 as n , we show that the giant component of G contains at least n - o ( n ) nodes with probability at least 1 - e - β n r n 2 for all n and for some positive constant β . We also obtain estimates on the diameter and number of the non-giant components of G .

Subclasses of typically real functions determined by some modular inequalities

Leopold Koczan, Katarzyna Trąbka-Więcław (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ : = { z : | z | < 1 } , normalized by f ( 0 ) = f ' ( 0 ) - 1 = 0 and such that Im z Im f ( z ) 0 for z Δ . Moreover, let us denote: T ( 2 ) : = { f T : f ( z ) = - f ( - z ) for z Δ } and T M , g : = { f T : f M g in Δ } , where M > 1 , g T S and S consists of all analytic functions, normalized and univalent in Δ .We investigate  classes in which the subordination is replaced with the majorization and the function g is typically real but does not necessarily univalent, i.e. classes { f T : f M g in Δ } , where M > 1 , g T , which we denote...

Contracting endomorphisms and dualizing complexes

Saeed Nasseh, Sean Sather-Wagstaff (2015)

Czechoslovak Mathematical Journal

Similarity:

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R . Our focus is on homological properties of contracting endomorphisms of R , e.g., the Frobenius endomorphism when R contains a field of positive characteristic. For instance, in this case, when R is F -finite and C is a semidualizing R -complex, we prove that the following conditions are equivalent: (i) C is a dualizing R -complex; (ii) C 𝐑 Hom R ( n R , C ) for some n > 0 ; (iii) G C -dim n R < and C is derived...

A localization property for B p q s and F p q s spaces

Hans Triebel (1994)

Studia Mathematica

Similarity:

Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

Explicit birational geometry of threefolds of general type, I

Jungkai A. Chen, Meng Chen (2010)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let V be a complex nonsingular projective 3-fold of general type. We prove P 12 ( V ) : = dim H 0 ( V , 12 K V ) &gt; 0 and P m 0 ( V ) &gt; 1 for some positive integer m 0 24 . A direct consequence is the birationality of the pluricanonical map ϕ m for all m 126 . Besides, the canonical volume Vol ( V ) has a universal lower bound ν ( 3 ) 1 63 · 126 2 .

Commutators of Marcinkiewicz integrals on Herz spaces with variable exponent

Hongbin Wang (2016)

Czechoslovak Mathematical Journal

Similarity:

Let Ω L s ( S n - 1 ) for s 1 be a homogeneous function of degree zero and b a BMO function. The commutator generated by the Marcinkiewicz integral μ Ω and b is defined by [ b , μ Ω ] ( f ) ( x ) = ( 0 | x - y | t Ω ( x - y ) | x - y | n - 1 [ b ( x ) - b ( y ) ] f ( y ) d y | 2 d t t 3 1 / 2 . In this paper, the author proves the ( L p ( · ) ( n ) , L p ( · ) ( n ) ) -boundedness of the Marcinkiewicz integral operator μ Ω and its commutator [ b , μ Ω ] when p ( · ) satisfies some conditions. Moreover, the author obtains the corresponding result about μ Ω and [ b , μ Ω ] on Herz spaces with variable exponent.

On linear preservers of two-sided gut-majorization on 𝐌 n , m

Asma Ilkhanizadeh Manesh, Ahmad Mohammadhasani (2018)

Czechoslovak Mathematical Journal

Similarity:

For X , Y 𝐌 n , m it is said that X is gut-majorized by Y , and we write X gut Y , if there exists an n -by- n upper triangular g-row stochastic matrix R such that X = R Y . Define the relation gut as follows. X gut Y if X is gut-majorized by Y and Y is gut-majorized by X . The (strong) linear preservers of gut on n and strong linear preservers of this relation on 𝐌 n , m have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of gut on n and 𝐌 n , m .