Pub Date : 2023-12-31DOI: 10.17323/1609-4514-2023-23-4-463-478
A. Bufetov
The aim of this note is to estimate the tail of the distribution of the number of particles in an interval under determinantal and Pfaffian point processes. The main result of the note is that the square of the number of particles under the determinantal point process whose correlation kernel is an entire function of finite order has sub-Poissonian tails. The same result also holds in the symplectic Pfaffian case. As a corollary, sub-Poissonian estimates are also obtained for exponential moments of additive functionals over pairs of particles.
{"title":"Sub-Poissonian Estimates for Exponential Moments of Additive Functionals over Pairs of Particles with Respect to Determinantal and Symplectic Pfaffian Point Processes Governed by Entire Functions","authors":"A. Bufetov","doi":"10.17323/1609-4514-2023-23-4-463-478","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-4-463-478","url":null,"abstract":"The aim of this note is to estimate the tail of the distribution of the number of particles in an interval under determinantal and Pfaffian point processes. The main result of the note is that the square of the number of particles under the determinantal point process whose correlation kernel is an entire function of finite order has sub-Poissonian tails. The same result also holds in the symplectic Pfaffian case. As a corollary, sub-Poissonian estimates are also obtained for exponential moments of additive functionals over pairs of particles.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"5 5","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139132799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.17323/1609-4514-2023-23-4-545-558
Askold Khovanskii, Leonid Monin
A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class of fibered toric varieties. Then we use them to illustrate some known and conjectural results on topology and intersection theory of general toric variety bundles. Finally, using the language of fibered toric varieties, we compute the equivariant cohomology rings of smooth complete toric varieties.
{"title":"Fibered Toric Varieties","authors":"Askold Khovanskii, Leonid Monin","doi":"10.17323/1609-4514-2023-23-4-545-558","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-4-545-558","url":null,"abstract":"A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class of fibered toric varieties. Then we use them to illustrate some known and conjectural results on topology and intersection theory of general toric variety bundles. Finally, using the language of fibered toric varieties, we compute the equivariant cohomology rings of smooth complete toric varieties.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139289942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-29DOI: 10.17323/1609-4514-2023-23-4-441-461
A. Blokh, L. Oversteegen, V. Timorin
A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) QL invariant filled Julia set $K^*$ such that $bin K^*$. In that case, exactly one critical point of $P$ does not belong to $K^*$. We show that if, in addition, the Julia set of $P$ has no (pre)periodic cutpoints, then this critical point is recurrent.
如果存在一个（连通的）QL不变填充朱利亚集$K^*$，使得$b/in K^*$，那么具有非排斥定点$b$的立方多项式$P$就可以说是立即可重正化的。在这种情况下，$P$ 恰好有一个临界点不属于 $K^*$。我们证明，如果此外 $P$ 的 Julia 集没有（前）周期切点，那么这个临界点就是经常出现的。
{"title":"Immediate Renormalization of Cubic Complex Polynomials with Empty Rational Lamination","authors":"A. Blokh, L. Oversteegen, V. Timorin","doi":"10.17323/1609-4514-2023-23-4-441-461","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-4-441-461","url":null,"abstract":"A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) QL invariant filled Julia set $K^*$ such that $bin K^*$. In that case, exactly one critical point of $P$ does not belong to $K^*$. We show that if, in addition, the Julia set of $P$ has no (pre)periodic cutpoints, then this critical point is recurrent.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"28 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139348566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-08DOI: 10.17323/1609-4514-2023-23-4-479-513
A. Glutsyuk
B.Josephson (Nobel Prize, 1973) predicted tunnelling effect for a system (called Josephson junction) of two superconductors separated by a narrow dielectric: existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by a family of differential equations on 2-torus depending on 3 parameters: $B$, $A$, $omega$. We study its rotation number $rho(B,A;omega)$ as a function of parameters. The three-dimensional phase-lock areas are the level sets $L_r:={rho=r}$ with non-empty interiors; they exist for $rinmathbb Z$ (Buchstaber, Karpov, Tertychnyi). For every fixed $omega>0$ and $rinmathbb Z$ the planar slice $L_rcap(mathbb R^2_{B,A}times{omega})$ is a garland of domains going vertically to infinity and separated by points; those separating points for which $Aneq0$ are called constrictions. In a joint paper by Yu.Bibilo and the author, it was shown that 1) at each constriction the rescaled abscissa $ell:=frac Bomega$ is equal to $rho$; 2) the family of constrictions with given $ellinmathbb Z$ is an analytic submanifold $Constr_ell$ in $(mathbb R^2_+)_{a,s}$, $a=omega^{-1}$, $s=frac Aomega$. Here we show that the limit points of $Constr_ell$ are $beta_{ell,k}=(0,s_{ell,k})$, where $s_{ell,k}>0$ are zeros of the Bessel function $J_ell(s)$, and it lands at them regularly. Known numerical pictures show that high components of $Int(L_r)$ look similar. In his paper with Bibilo, the author introduced a candidate to the self-similarity map between neighbor components: the Poincar'e map of the dynamical isomonodromic foliation governed by Painlev'e 3 equation. Whenever well-defined, it preserves $rho$. We show that the Poincar'e map is well-defined on a neighborhood of the plane ${ a=0}subsetmathbb R^2_{ell,a}times(mathbb R_+)_s$, and it sends $beta_{ell,k}$ to $beta_{ell,k+1}$ for integer $ell$.
{"title":"On Germs of Constriction Curves in Model of Overdamped Josephson Junction, Dynamical Isomonodromic Foliation and Painlevé 3 Equation","authors":"A. Glutsyuk","doi":"10.17323/1609-4514-2023-23-4-479-513","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-4-479-513","url":null,"abstract":"B.Josephson (Nobel Prize, 1973) predicted tunnelling effect for a system (called Josephson junction) of two superconductors separated by a narrow dielectric: existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by a family of differential equations on 2-torus depending on 3 parameters: $B$, $A$, $omega$. We study its rotation number $rho(B,A;omega)$ as a function of parameters. The three-dimensional phase-lock areas are the level sets $L_r:={rho=r}$ with non-empty interiors; they exist for $rinmathbb Z$ (Buchstaber, Karpov, Tertychnyi). For every fixed $omega>0$ and $rinmathbb Z$ the planar slice $L_rcap(mathbb R^2_{B,A}times{omega})$ is a garland of domains going vertically to infinity and separated by points; those separating points for which $Aneq0$ are called constrictions. In a joint paper by Yu.Bibilo and the author, it was shown that 1) at each constriction the rescaled abscissa $ell:=frac Bomega$ is equal to $rho$; 2) the family of constrictions with given $ellinmathbb Z$ is an analytic submanifold $Constr_ell$ in $(mathbb R^2_+)_{a,s}$, $a=omega^{-1}$, $s=frac Aomega$. Here we show that the limit points of $Constr_ell$ are $beta_{ell,k}=(0,s_{ell,k})$, where $s_{ell,k}>0$ are zeros of the Bessel function $J_ell(s)$, and it lands at them regularly. Known numerical pictures show that high components of $Int(L_r)$ look similar. In his paper with Bibilo, the author introduced a candidate to the self-similarity map between neighbor components: the Poincar'e map of the dynamical isomonodromic foliation governed by Painlev'e 3 equation. Whenever well-defined, it preserves $rho$. We show that the Poincar'e map is well-defined on a neighborhood of the plane ${ a=0}subsetmathbb R^2_{ell,a}times(mathbb R_+)_s$, and it sends $beta_{ell,k}$ to $beta_{ell,k+1}$ for integer $ell$.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"79 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.17323/1609-4514-2023-23-1-1-9
H. Alzer, M. Kwong
{"title":"On a One-Parameter Class of Cosine Polynomials","authors":"H. Alzer, M. Kwong","doi":"10.17323/1609-4514-2023-23-1-1-9","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-1-1-9","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42396376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.17323/1609-4514-2023-23-1-121-128
J. Rifà, V. Zinoviev
{"title":"On Binary Quadratic Symmetric Bent and Semi-Bent Functions","authors":"J. Rifà, V. Zinoviev","doi":"10.17323/1609-4514-2023-23-1-121-128","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-1-121-128","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48550437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.17323/1609-4514-2023-23-3-319-330
Frédéric Campana
. We show, using [14], that a smooth projective fibration f : X → Y between connected complex quasi-projective manifolds satisfies the equality κ ( X ) = κ ( X y ) + κ ( Y ) of Logarithmic Kodaira dimensions if its fibres X y admit a good minimal model. Without the last assumption, this was conjectured in [11]. Sev-eral cases are established in [13], which inspired the present text. Although the present results overlap with those of [13] in the projective case, the approach here is different, based on the rôle played by birationally isotrivial fibrations, special manifolds and the core map of Y introduced and constructed in [3].
{"title":"Kodaira Additivity, Birational Isotriviality, and Specialness","authors":"Frédéric Campana","doi":"10.17323/1609-4514-2023-23-3-319-330","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-3-319-330","url":null,"abstract":". We show, using [14], that a smooth projective fibration f : X → Y between connected complex quasi-projective manifolds satisfies the equality κ ( X ) = κ ( X y ) + κ ( Y ) of Logarithmic Kodaira dimensions if its fibres X y admit a good minimal model. Without the last assumption, this was conjectured in [11]. Sev-eral cases are established in [13], which inspired the present text. Although the present results overlap with those of [13] in the projective case, the approach here is different, based on the rôle played by birationally isotrivial fibrations, special manifolds and the core map of Y introduced and constructed in [3].","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"14 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.17323/1609-4514-2023-23-2-271-282
Khudoyor Mamayusupov
{"title":"Accesses to Parabolic Fixed Point from its Immediate Basin","authors":"Khudoyor Mamayusupov","doi":"10.17323/1609-4514-2023-23-2-271-282","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-2-271-282","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.17323/1609-4514-2023-23-3-285-307
Vladimir I. Bogachev, Svetlana N. Popova, A. V. Rezbaev
{"title":"On Nonlinear Kantorovich Problems with Density Constraints","authors":"Vladimir I. Bogachev, Svetlana N. Popova, A. V. Rezbaev","doi":"10.17323/1609-4514-2023-23-3-285-307","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-3-285-307","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.17323/1609-4514-2023-23-3-331-367
Péter Major
{"title":"The Theory of Wiener–Itô Integrals in Vector-Valued Gaussian Stationary Random Fields. Part II","authors":"Péter Major","doi":"10.17323/1609-4514-2023-23-3-331-367","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-3-331-367","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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