Probability Theory and Related Fields最新文献

{"title":"Large deviation principle for quasi-stationary distributions and multiscale dynamics of absorbed singular diffusions","authors":"Weiwei Qi, Zhongwei Shen, Yingfei Yi","doi":"10.1007/s00440-023-01246-0","DOIUrl":"https://doi.org/10.1007/s00440-023-01246-0","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"39 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139007053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetric cooperative motion in one dimension","authors":"Louigi Addario-Berry, Erin Beckman, Jessica Lin","doi":"10.1007/s00440-023-01244-2","DOIUrl":"https://doi.org/10.1007/s00440-023-01244-2","url":null,"abstract":"<p>We explore the relationship between recursive distributional equations and convergence results for finite difference schemes of parabolic partial differential equations (PDEs). We focus on a family of random processes called symmetric cooperative motions, which generalize the symmetric simple random walk and the symmetric hipster random walk introduced in Addario-Berry et al. (Probab Theory Related fields 178(1–2):437–473, 2020). We obtain a distributional convergence result for symmetric cooperative motions and, along the way, obtain a novel proof of the Bernoulli central limit theorem. In addition, we prove a PDE result relating distributional solutions and viscosity solutions of the porous medium equation and the parabolic <i>p</i>-Laplace equation, respectively, in one dimension.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"58 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fleming–Viot couples live forever","authors":"Mateusz Kwaśnicki","doi":"10.1007/s00440-023-01247-z","DOIUrl":"https://doi.org/10.1007/s00440-023-01247-z","url":null,"abstract":"<p>We prove a non-extinction result for Fleming–Viot-type systems of two particles with dynamics described by an arbitrary symmetric Hunt process under the assumption that the reference measure is finite. Additionally, we describe an invariant measure for the system, we discuss its ergodicity, and we prove that the reference measure is a stationary measure for the embedded Markov chain of positions of the surviving particle at successive branching times.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"12 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the ergodicity of interacting particle systems under number rigidity","authors":"Kohei Suzuki","doi":"10.1007/s00440-023-01243-3","DOIUrl":"https://doi.org/10.1007/s00440-023-01243-3","url":null,"abstract":"<p>In this paper, we provide relations among the following properties: </p><ol>\u0000<li>\u0000<span>(a)</span>\u0000<p>the tail triviality of a probability measure <span>(mu )</span> on the configuration space <span>({varvec{Upsilon }})</span>;</p>\u0000</li>\u0000<li>\u0000<span>(b)</span>\u0000<p>the finiteness of a suitable <span>(L^2)</span>-transportation-type distance <span>(bar{textsf {d} }_{varvec{Upsilon }})</span>;</p>\u0000</li>\u0000<li>\u0000<span>(c)</span>\u0000<p>the irreducibility of local <span>({mu })</span>-symmetric Dirichlet forms on <span>({varvec{Upsilon }})</span>.</p>\u0000</li>\u0000</ol><p> As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/permanental point processes including <span>(text {sine}_{2})</span>, <span>(text {Airy}_{2})</span>, <span>(text {Bessel}_{alpha , 2})</span> (<span>(alpha ge 1)</span>), and <span>(text {Ginibre})</span> point processes. In particular, the case of the unlabelled Dyson Brownian motion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh–Peres plays a key role.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"314 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Retrospective Cohort Study on the Surgical Outcomes of Intracapsular Thyroidectomy Vs Standard Thyroidectomy.","authors":"S Meenakshi, M K Rajasekar, Sumitha Ramanathan","doi":"10.1007/s12070-023-04074-9","DOIUrl":"10.1007/s12070-023-04074-9","url":null,"abstract":"<p><p>The focal point of thyroidectomy surgery has always been to reduce the incidence of inadvertent damage to the recurrent laryngeal nerve(RLN). The intracapsular thyroidectomy is one such technique with minimum chance of injuring the nerve. To compare retrospectively the surgical outcomes between the two methods of thyroidectomy-coventional thyroidectomy Vs intracapsular thyroidectomy. Materials and methods-55 cases of benign thyroid disease for whom thyroidectomy was performed in our hospital between the period of 2019-2022 were compared retrospectively. Out of these 34 cases had undergone intracapsular thyroidectomy and 21 cases underwent routine extracapsular thyroidectomy. The surgical outcomes including operation time, pain, postoperative infection, postoperative hypocalcemia, postoperative recurrent laryngeal nerve paralysis and mean hospital stay were analyzed. The mean operating time were very low in the intracapsular limb as compared to the other group. The pain and the mean hospital stay was also far lesser for the intracapsular limb. Both cohorts had no incidence of hypocalcemia. The incidence of recurrent laryngeal nerve palsy was very low in the intracapsular cohort (only 1 case of temporary unilateral RLN palsy), whereas it was higher in the routine extracapsular cohort (5 cases of permanent palsy). The risk of having vocal cord palsy (left/right) is 1.172 times more with conventional/standard thyroidectomy as compared to intracapsular thyroidectomy. Intracapsular technique is a much more rewarding method to perform thyroidectomy, without the risk of the recurrent laryngeal nerve palsy as compared to routine thyroidectomy.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"175 1","pages":"3792-3797"},"PeriodicalIF":1.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10645788/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73759487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Half-space depth of log-concave probability measures","authors":"Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis","doi":"10.1007/s00440-023-01236-2","DOIUrl":"https://doi.org/10.1007/s00440-023-01236-2","url":null,"abstract":"<p>Given a probability measure <span>(mu )</span> on <span>({{mathbb {R}}}^n)</span>, Tukey’s half-space depth is defined for any <span>(xin {{mathbb {R}}}^n)</span> by <span>(varphi _{mu }(x)=inf {mu (H):Hin {{{mathcal {H}}}}(x)})</span>, where <span>(mathcal{H}(x))</span> is the set of all half-spaces <i>H</i> of <span>({{mathbb {R}}}^n)</span> containing <i>x</i>. We show that if <span>(mu )</span> is a non-degenerate log-concave probability measure on <span>({{mathbb {R}}}^n)</span> then </p><span>$$begin{aligned} e^{-c_1n}leqslant int _{{mathbb {R}}^n}varphi _{mu }(x),dmu (x) leqslant e^{-c_2n/L_{mu }^2} end{aligned}$$</span><p>where <span>(L_{mu })</span> is the isotropic constant of <span>(mu )</span> and <span>(c_1,c_2&gt;0)</span> are absolute constants. The proofs combine large deviations techniques with a number of facts from the theory of <span>(L_q)</span>-centroid bodies of log-concave probability measures. The same ideas lead to general estimates for the expected measure of random polytopes whose vertices have a log-concave distribution.\u0000</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"314 2","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Edge statistics for lozenge tilings of polygons, I: concentration of height function on strip domains","authors":"Jiaoyang Huang","doi":"10.1007/s00440-023-01238-0","DOIUrl":"https://doi.org/10.1007/s00440-023-01238-0","url":null,"abstract":"","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"29 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134991930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Harnack inequality and one-endedness of UST on reversible random graphs","authors":"Nathanaël Berestycki, Diederik van Engelenburg","doi":"10.1007/s00440-023-01239-z","DOIUrl":"https://doi.org/10.1007/s00440-023-01239-z","url":null,"abstract":"Abstract We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequality, and (d) one-endedness of the wired uniform spanning tree. In particular this gives a proof of the anchored (and in fact also elliptic) Harnack inequality on the UIPT. This also complements and strengthens some results of Benjamini et al. (Ann Probab 29(1):1–65, 2001). Furthermore, we make progress towards a conjecture of Aldous and Lyons by proving that these conditions are fulfilled for strictly subdiffusive recurrent unimodular graphs. Finally, we discuss the behaviour of the random walk conditioned to never return to the origin, which is well defined as a consequence of our results.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":" 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal transport methods for combinatorial optimization over two random point sets","authors":"Michael Goldman, Dario Trevisan","doi":"10.1007/s00440-023-01245-1","DOIUrl":"https://doi.org/10.1007/s00440-023-01245-1","url":null,"abstract":"Abstract We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $$mathbb {R}^d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:math> where the edge cost between two points is given by a p th power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and $$d ge 3, 1le p<d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:math> . Previous results were limited to the range $$p<d/2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>d</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . Our proofs are based on subadditivity methods and build upon new bounds for random instances of the Euclidean bipartite matching problem, obtained through its optimal transport relaxation and functional analytic techniques.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"37 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135430948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the lack of Gaussian tail for rough line integrals along fractional Brownian paths","authors":"H. Boedihardjo, X. Geng","doi":"10.1007/s00440-023-01242-4","DOIUrl":"https://doi.org/10.1007/s00440-023-01242-4","url":null,"abstract":"Abstract We show that the tail probability of the rough line integral $$int _{0}^{1}phi (X_{t})dY_{t}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mn>1</mml:mn> </mml:msubsup> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> </mml:math> , where ( X , Y ) is a 2D fractional Brownian motion with Hurst parameter $$Hin (1/4,1/2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$phi $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ϕ</mml:mi> </mml:math> is a $$C_{b}^{infty }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mi>∞</mml:mi> </mml:msubsup> </mml:math> -function satisfying a mild non-degeneracy condition on its derivative, cannot decay faster than a $$gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>γ</mml:mi> </mml:math> -Weibull tail with any exponent $$gamma &gt;2H+1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>2</mml:mn> <mml:mi>H</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . In particular, this produces a simple class of examples of differential equations driven by fBM, whose solutions fail to have Gaussian tail even though the underlying vector fields are assumed to be of class $$C_{b}^{infty }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mi>∞</mml:mi> </mml:msubsup> </mml:math> . This also demonstrates that the well-known upper tail estimate proved by Cass–Litterer–Lyons in 2013 is essentially sharp.","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":"23 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136106006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}